Matrices and Determinants

Comprehensive Question Bank & Study Notes

Multiple Choice Questions

1 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2025
#788
If
\[
A =
\begin{bmatrix}
-1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{bmatrix},
\]
then \(A^{-1}\) is
(A) \begin{bmatrix} -1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1 \end{bmatrix}
(B) \begin{bmatrix} 1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1 \end{bmatrix}
(C) \begin{bmatrix} -1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1 \end{bmatrix}
(D) \begin{bmatrix} -1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}
MEDIUM
2 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2025
#787
A is a square matrix of order 2 such that det(A)=4 , then det(4adjA) is
(A) 16
(B) 64
(C) 256
(D) 512
MEDIUM
3 Knowledge REMEMBER MCQ_SINGLE 1 Mark(s) 2025
#770
The matrix \(A=\begin{bmatrix}\sqrt{3}&0&0\\ 0&\sqrt{2}&0\\ 0&0&\sqrt{5}\end{bmatrix}\) is a/an:
(A) scalar matrix
(B) identity matrix
(C) null matrix
(D) symmetric matrix
EASY
4 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2025
#767
If \(\begin{bmatrix}2x-1&3x\\ 0&y^{2}-1\end{bmatrix}=\begin{bmatrix}x+3&12\\ 0&35\end{bmatrix},\) then the value of \((x-y)\) is :
(A) 2 or 10
(B) 2 or 10
(C) 2 or - 10
(D) -2 or - 10
MEDIUM
5 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2025
#766
Let
\[
A = \begin{pmatrix}
1 & -2 & -1 \\
0 & 4 & -1 \\
-3 & 2 & 1
\end{pmatrix}, \quad
B = \begin{pmatrix}
-2 \\
-5 \\
-7
\end{pmatrix}, \quad
C = \begin{pmatrix}
9 & 8 & 7
\end{pmatrix},
\]
which of the following is defined?
(A) Only AB
(B) Only AC
(C) Only BA
(D) All AB, AC and BA
MEDIUM
6 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2025
#765
If
\[
A = \begin{pmatrix}
7 & 0 & x \\
0 & 7 & 0 \\
0 & 0 & y
\end{pmatrix}
\]
is a scalar matrix, then \(y^x\) is equal to
(A) \(0\)
(B) \(1\)
(C) \(7\)
(D) \(\pm 7\)
MEDIUM
7 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2025
#764
If \(A\) and \(B\) are invertible matrices, then which of the following is \underline{not correct}?
(A) \((A + B)^{-1} = B^{-1} + A^{-1}\)
(B) \((AB)^{-1} = B^{-1} A^{-1}\)
(C) \(\text{adj}(A) = |A| A^{-1}\)
(D) \(|A^{-1}| = |A|^{-1}\)
MEDIUM
8 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2025
#763
If \(A=\begin{bmatrix}1&12&4y\\ 6x&5&2x\\ 8x&4&6\end{bmatrix}\) is a symmetric matrix, then \((2x+y)\) is
(A) \(-8\)
(B) 0
(C) 6
(D) 8
MEDIUM
9 Knowledge UNDERSTAND MCQ_SINGLE 1 Mark(s) 2025
#762
Which of the following can be both a symmetric and skew-symmetric matrix ?
(A) Unit Matrix
(B) Diagonal Matrix
(C) Null Matrix
(D) Row Matrix
EASY
10 Competency APPLY MCQ_SINGLE 1 Mark(s) 2025
#761
Four friends Abhay, Bina, Chhaya and Devesh were asked to simplify \(4~AB+3(AB+BA)-4~BA,\) where A and B are both matrices of order \(2\times2\). <p>It is known that \(A\ne B\ne I\) and \(A^{-1}\ne B\). <p>Their answers are given as: <p>Abhay: \(6 AB\), <p>Bina : \(7 AB-BA\), <p>Chhaya: \(8 AB\), <p>Devesh: \(7 BA - AB\).<p> Who answered it correctly?
(A) Abhay
(B) Bina
(C) Chhaya
(D) Devesh
MEDIUM
11 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2025
#760
If A and B are square matrices of order m such that \(A^{2}-B^{2}=(A-B)(A+B),\) then which of the following is always correct?
(A) \(A=B\)
(B) \(AB=BA\)
(C) \(A=0\) or \(B=0\)
(D) \(A=I\) or \(B=I\)
MEDIUM
12 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2025
#759
If M and N are square matrices of order 3 such that det \((M)=m\) and \(MN=mI,\) then det (N) is equal to:
(A) -1
(B) 1
(C) \(-m^{2}\)
(D) \(m^{2}\)
MEDIUM
13 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2025
#758
If \(A=\begin{bmatrix}1&2&3\\ -4&3&7\end{bmatrix}\) and \(B=\begin{bmatrix}4&3\\ -1&2\\ 0&5\end{bmatrix},\) then the correct statement is:
(A) Only AB is defined.
(B) Only BA is defined.
(C) AB and BA, both are defined.
(D) AB and BA, both are not defined.
MEDIUM
14 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2025
#757
If \(\begin{vmatrix}2x&5\\ 12&x\end{vmatrix}=\begin{vmatrix}6&-5\\ 4&3\end{vmatrix}\) then the value of x is:
(A) 3
(B) 7
(C) \(\pm7\)
(D) \(\pm3\)
MEDIUM
15 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2025
#756
If \(A=[a_{ij}]\) is a \(3\times3\) diagonal matrix such that \(a_{11}=1\), \(a_{22}=5\) and \(a_{33}=-2\), then \(|A|\) is:
(A) 0
(B) -10
(C) 10
(D) 1
MEDIUM
16 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2025
#755
If \(\begin{bmatrix}4+x&x-1\\ -2&3\end{bmatrix}\) is a singular matrix, then the value of x is:
(A) 0
(B) 1
(C) -2
(D) 4
MEDIUM
17 Knowledge UNDERSTAND MCQ_SINGLE 1 Mark(s) 2025
#754
Let both \(AB^{\prime}\) and \(B^{\prime}A\) be defined for matrices A and B. If order of A is \(n\times m\), then the order of B is:
(A) \(n\times n\)
(B) \(n\times m\)
(C) \(m\times m\)
(D) \(m\times n\)
MEDIUM
18 Knowledge REMEMBER MCQ_SINGLE 1 Mark(s) 2025
#753
If \(A=\begin{bmatrix}-1&0&0\\ 0&3&0\\ 0&0&5\end{bmatrix},\) then A is a/an:
(A) scalar matrix
(B) identity matrix
(C) symmetric matrix
(D) skew-symmetric matrix
EASY
19 Knowledge UNDERSTAND MCQ_SINGLE 1 Mark(s) 2025
#752
Sum of two skew-symmetric matrices of same order is always a/an:
(A) skew-symmetric matrix
(B) symmetric matrix
(C) null matrix
(D) identity matrix
MEDIUM
20 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2025
#751
What is the total number of possible matrices of order \(3\times3\) with each entry as \(\sqrt{2}\) or \(\sqrt{3}\)?
(A) 9
(B) 512
(C) 615
(D) 64
MEDIUM
21 Knowledge REMEMBER MCQ_SINGLE 1 Mark(s) 2025
#750
The matrix \(A=\begin{bmatrix}\sqrt{3}&0&0\\ 0&\sqrt{2}&0\\ 0&0&\sqrt{5}\end{bmatrix}\) is a/an:
(A) scalar matrix
(B) identity matrix
(C) null matrix
(D) symmetric matrix
EASY
22 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2025
#749
If A and B are two square matrices each of order 3 with \(|A|=3\) and \(|B|=5\), then \(|2AB|\) is:
(A) 30
(B) 120
(C) 15
(D) 225
MEDIUM
23 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2025
#748
Let A be a square matrix of order 3. If \(|A|=5\), then \(|\operatorname{adj} A|\) is:
(A) 5
(B) 125
(C) 25
(D) -5
MEDIUM
24 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2025
#747
If \(\begin{bmatrix}2x-1&3x\\ 0&y^{2}-1\end{bmatrix}=\begin{bmatrix}x+3&12\\ 0&35\end{bmatrix},\) then the value of \((x-y)\) is :
(A) 2 or 10
(B) 2 or 10
(C) 2 or - 10
(D) -2 or - 10
MEDIUM
25 Knowledge REMEMBER MCQ_SINGLE 1 Mark(s) 2024
#746
If a matrix has 36 elements, the number of possible orders it can have, is:
(A) 13
(B) 3
(C) 5
(D) 9
EASY
26 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2024
#745
If \(\begin{bmatrix}x+y&2\\ 5&xy\end{bmatrix}=\begin{bmatrix}6&2\\ 5&8\end{bmatrix},\) then the value of \((\frac{24}{x}+\frac{24}{y})\) is:
(A) 7
(B) 6
(C) 8
(D) 18
MEDIUM
27 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2024
#744
\(\begin{vmatrix}x+1&x-1\\ x^{2}+x+1&x^{2}-x+1\end{vmatrix}\) is equal to:
(A) \(2x^{3}\)
(B) 2
(C) 0
(D) \(2x^{3}-2\)
MEDIUM
28 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2024
#743
If A and B are two non-zero square matrices of same order such that \((A+B)^{2}=A^{2}+B^{2}\) then :
(A) \(AB=O\)
(B) \(AB=-BA\)
(C) \(BA=O\)
(D) \(AB=BA\)
MEDIUM
29 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2024
#742
If the sum of all the elements of a \(3\times3\) scalar matrix is 9, then the product of all its elements is:
(A) 0
(B) 9
(C) 27
(D) 729
MEDIUM
30 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2024
#741
If \(\begin{vmatrix}-a&b&c\\ a&-b&c\\ a&b&-c\end{vmatrix}= kabc,\) then the value of k is:
(A) 0
(B) 1
(C) 2
(D) 4
MEDIUM
31 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2024
#740
If \(A=[a_{ij}]\) be a \(3\times3\) matrix, where \(a_{ij}=i-3j\), then which of the following is false ?
(A) \(a_{11}\lt0\)
(B) \(a_{12}+a_{21}=-6\)
(C) \(a_{13}\gt a_{31}\)
(D) \(a_{31}=0\)
MEDIUM
32 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2024
#739
If \(F(x)=\begin{bmatrix}\cos~x&-\sin~x&0\\ \sin~x&\cos~x&0\\ 0&0&1\end{bmatrix}\) and \([F(x)]^{2}=F(kx)\), then the value of k is :
(A) 1
(B) 2
(C) 0
(D) -2
MEDIUM
33 Knowledge UNDERSTAND MCQ_SINGLE 1 Mark(s) 2024
#738
If \(A=[a_{ij}]\) is an identity matrix, then which of the following is true ?
(A) \(a_{ij}=\begin{cases}0,&if~i=j\\ 1,&if~i\ne j\end{cases}\)
(B) \(a_{ij}=1,\forall i,j\)
(C) \(a_{ij}=0,\forall i,j\)
(D) \(a_{ij}=\begin{cases}0,&if~i\ne j\\ 1,&if~i=j\end{cases}\)
EASY
34 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2024
#737
Let \(A=\begin{bmatrix}a&b\\ c&d\end{bmatrix}\) be a square matrix such that adj \(A=A\) Then, \((a+b+c+d)\) is equal to :
(A) 2a
(B) 2b
(C) 2c
(D) 0
HARD
35 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2024
#736
If A and B are two skew symmetric matrices, then \((AB+BA)\) is :
(A) a skew symmetric matrix
(B) a symmetric matrix
(C) a null matrix
(D) an identity matrix
MEDIUM
36 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2024
#735
If \(A=\begin{bmatrix}2&0&0\\ 0&3&0\\ 0&0&5\end{bmatrix},\) then \(A^{-1}\) is:
(A) \([\begin{matrix}\frac{1}{2}&0&0\\ 0&3&0\\ 0&0&\frac{1}{5}\end{matrix}]\)
(B) \(30[\begin{matrix}\frac{1}{2}&0&0\\ 0&\frac{1}{3}&0\\ 0&0&\frac{1}{5}\end{matrix}]\)
(C) \(\frac{1}{30}[\begin{matrix}2&0&0\\ 0&3&0\\ 0&0&5\end{matrix}]\)
(D) \(\frac{1}{30}[\begin{matrix}\frac{1}{2}&0&0\\ 0&\frac{1}{3}&0\\ 0&0&\frac{1}{5}\end{matrix}]\)
MEDIUM
37 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2024
#734
\(If\begin{bmatrix}a&c&0\\ b&d&0\\ 0&0&5\end{bmatrix}\) is a scalar matrix, then the value of \(a+2b+3c+4d\) is:
(A) 0
(B) 5
(C) 10
(D) 25
MEDIUM
38 Knowledge UNDERSTAND MCQ_SINGLE 1 Mark(s) 2024
#733
Given that \(A^{-1}=\frac{1}{7}\begin{bmatrix}2&1\\ -3&2\end{bmatrix}\) matrix A is
(A) \(7[\begin{matrix}2&-1\\ 3&2\end{matrix}]\)
(B) \([\begin{matrix}2&-1\\ 3&2\end{matrix}]\)
(C) \(\frac{1}{7}[\begin{matrix}2&-1\\ 3&2\end{matrix}]\)
(D) \(\frac{1}{49}[\begin{matrix}2&-1\\ 3&2\end{matrix}]\)
MEDIUM
39 Competency APPLY MCQ_SINGLE 1 Mark(s) 2024
#732
\(If~A=[\begin{matrix}2&1\\ -4&-2\end{matrix}].\) then the value of \(I-A+A^{2}-A^{3}+...is\): <span class="marks">(1)</span>
(A) \([\begin{matrix}-1&-1\\ 4&3\end{matrix}]\)
(B) \([\begin{matrix}3&1\\ -4&-1\end{matrix}]\)
(C) \([\begin{matrix}0&0\\ 0&0\end{matrix}]\)
(D) \([\begin{matrix}1&0\\ 0&1\end{matrix}]\)
MEDIUM
40 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2024
#731
\(If~A=\begin{bmatrix}-2&0&0\\ 1&2&3\\ 5&1&-1\end{bmatrix},\) then the value of | A (adj. A) | is:
(A) 100 I
(B) 10 I
(C) 10
(D) 1000
MEDIUM
41 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2024
#730
Given that \([\begin{matrix}1&x\end{matrix}]\begin{bmatrix}4&0\\ -2&0\end{bmatrix}=0,\) the value of x is:
(A) -4
(B) -2
(C) 2
(D) 4
MEDIUM
42 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2024
#729
If A is a square matrix of order 3 such that the value of \(|adj\cdot A|=8,\) then the value of \(|A^{T}|\) is: <span class="marks">(1)</span>
(A) \(\sqrt{2}\)
(B) \(-\sqrt{2}\)
(C) 8
(D) \(2\sqrt{2}\)
MEDIUM
43 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2024
#728
If \(\begin{bmatrix}x&2&0\end{bmatrix}\begin{bmatrix}5\\ -1\\ x\end{bmatrix}=\begin{bmatrix}3&1\end{bmatrix}\begin{bmatrix}-2\\ x\end{bmatrix},\) then value of x is:
(A) -1
(B) 0
(C) 1
(D) 2
MEDIUM
44 Competency APPLY MCQ_SINGLE 1 Mark(s) 2024
#727
Find the matrix \(A^{2}\), where \(A=[a_{ij}]\) is a \(2\times2\) matrix whose elements are given by \(a_{ij}=\) maximum (i, j) - minimum (i, j):
(A) \([\begin{matrix}0&0\\ 0&0\end{matrix}]\)
(B) \([\begin{matrix}1&0\\ 0&1\end{matrix}]\)
(C) \([\begin{matrix}0&1\\ 1&0\end{matrix}]\)
(D) \([\begin{matrix}1&1\\ 1&1\end{matrix}]\)
MEDIUM
45 Knowledge UNDERSTAND MCQ_SINGLE 1 Mark(s) 2023
#853
Let A be the area of a triangle having vertices $(x_1, y_1), (x_2, y_2)$ and $(x_3, y_3)$. Which of the following is correct?
(A) $|\begin{matrix}x_{1}&y_{1}&1\\ x_{2}&y_{2}&1\\ x_{3}&y_{3}&1\end{matrix}|=\pm A$
(B) $|\begin{matrix}x_{1}&y_{1}&1\\ x_{2}&y_{2}&1\\ x_{3}&y_{3}&1\end{matrix}|=\pm2A$
(C) $|\begin{matrix}x_{1}&y_{1}&1\\ x_{2}&y_{2}&1\\ x_{3}&y_{3}&1\end{matrix}|=\pm\frac{A}{2}$
(D) $|\begin{matrix}x_{1}&y_{1}&1\\ x_{2}&y_{2}&1\\ x_{3}&y_{3}&1\end{matrix}|^{2}=A^{2}$
MEDIUM
46 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2023
#852
5. The value $|\begin{matrix}x+y & y+z & z+x\\ z & x & y\\ 1 & 1 & 1\end{matrix}|$ is :
(A) 0
(B) 1
(C) $x+y+z$
(D) $2(x+y+z)$
MEDIUM
47 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2023
#851
Let A be a 3\times3 matrix such that | adj A|=64. Then |A| is equal to:
(A) 8 only
(B) \- 8 only
(C) 64
(D) 8 or-8
MEDIUM
48 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2023
#850
If |A|=2, where A is a 2\times2 matrix, then |4A^{-1}| equals :
(A) 4
(B) 2
(C) 8
(D) \frac{1}{32}
MEDIUM
49 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2023
#849
If |(a, 3, 4), (1, 2, 1), (1, 4, 1)| = 0, then the value of a is
(A) 1
(B) 2
(C) 3
(D) 4
MEDIUM
50 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2023
#848
For what value of $x\in[0,\frac{\pi}{2}]$, is $A+A'=\sqrt{3}I$, where $A=\begin{bmatrix}\cos x & \sin x\\ -\sin x & \cos x\end{bmatrix}$ ?
(A) $\frac{\pi}{3}$
(B) $\frac{\pi}{6}$
(C) $0$
(D) $\frac{\pi}{2}$
MEDIUM
51 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2023
#847
A and B are skew-symmetric matrices of same order. AB is symmetric, if:
(A) $AB=O$
(B) $AB=-BA$
(C) $AB=BA$
(D) $BA=O$
MEDIUM
52 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2023
#846
If $A\cdot(\text{adj }A)=\begin{bmatrix}3&0&0\\ 0&3&0\\ 0&0&3\end{bmatrix}$, then the value of $|A|+| ext{adj }A|$ is equal to :
(A) 12
(B) 9
(C) 3
(D) 27
MEDIUM
53 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2023
#845
If $A=\begin{bmatrix}1&4&x\\ z&2&y\\ -3&-1&3\end{bmatrix}$ is a symmetric matrix, then the value of $x+y+z$ is :
(A) 10
(B) 6
(C) 8
(D) 0
MEDIUM
54 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2023
#844
4. If a matrix $A=\begin{bmatrix}1 & 2 & 3\end{bmatrix}$, then the matrix $AA'$ (where $A'$ is the transpose of A) is:
(A) 14
(B) $\begin{bmatrix}1 & 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 3\end{bmatrix}$
(C) $\begin{bmatrix}1 & 2 & 3\\ 2 & 3 & 1\\ 3 & 1 & 2\end{bmatrix}$
(D) $\begin{bmatrix}14\end{bmatrix}$
MEDIUM
55 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2023
#843
3. If A is a square matrix and $A^{2}=A$ then $(I+A)^{2}-3A$ is equal to :
(A) I
(B) A
(C) 2A
(D) 3I
MEDIUM
56 Knowledge UNDERSTAND MCQ_SINGLE 1 Mark(s) 2023
#842
2. The product $\begin{bmatrix}a & b\\ -b & a\end{bmatrix}\begin{bmatrix}a & -b\\ b & a\end{bmatrix}$ is equal to :
(A) $\begin{bmatrix}a^{2}+b^{2} & 0\\ 0 & a^{2}+b^{2}\end{bmatrix}$
(B) $\begin{bmatrix}(a+b)^{2} & 0\\ (a+b)^{2} & 0\end{bmatrix}$
(C) $\begin{bmatrix}a^{2}+b^{2} & 0\\ a^{2}+b^{2} & 0\end{bmatrix}$
(D) $\begin{bmatrix}a & 0\\ 0 & b\end{bmatrix}$
EASY
57 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2023
#841
1. If $x\begin{bmatrix}1\\ 2\end{bmatrix}+y\begin{bmatrix}2\\ 5\end{bmatrix}=\begin{bmatrix}4\\ 9\end{bmatrix}$, then
(A) $x=1, y=2$
(B) $x=2, y=1$
(C) $x=1, y=-1$
(D) $x=3, y=2$
MEDIUM
58 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2023
#840
If A=\begin{bmatrix}0&1\\ -1&0\end{bmatrix} and (3\~I+4\~A)(3\~I-4\~A)=x^{2}I, then the value(s) x is/are:
(A) \pm\sqrt{7}
(B) 0
(C) \pm5
(D) 25
MEDIUM
59 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2023
#839
If A=\begin{bmatrix}3&4\\ 5&2\end{bmatrix} and 2A+B is a null matrix, then B is equal to :
(A) \begin{bmatrix}6&8\\ 10&4\end{bmatrix}
(B) \begin{bmatrix}-6&-8\\ -10&-4\end{bmatrix}
(C) \begin{bmatrix}5&8\\ 10&3\end{bmatrix}
(D) \begin{bmatrix}-5&-8\\ -10&-3\end{bmatrix}
EASY
60 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2023
#838
If for a square matrix A, A^{2}-3A+I=O and A^{-1}=xA+yI, then the value of x+y is:
(A) \-2
(B) 2
(C) 3
(D) -3
MEDIUM
61 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2023
#837
If A=[(1, 0), (2, 1)], B=[(x, 0), (1, 1)] and A=B², then x equals
(A) ±1
(B) -1
(C) 1
(D) 2
MEDIUM
62 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2023
#836
If for a square matrix A, A² - A + I = O then A⁻¹ equals
(A) A
(B) A+I
(C) I-A
(D) A-I
MEDIUM

Short Answer (3 Marks)

1 Knowledge APPLY SA 3 Mark(s) 2023
#888
If A=[(1, 2, 3), (3, -2, 1), (4, 2, 1)], then show that A³ - 23A - 40I = O.
MEDIUM

Long Answer (5 Marks)

1 Knowledge APPLY LA 5 Mark(s) 2023
#924
If $A=\begin{bmatrix}1&2&-2\\ -1&3&0\\ 0&-2&1\end{bmatrix}$ and $B^{-1}=\begin{bmatrix}3&-1&1\\ -15&6&-5\\ 5&-2&2\end{bmatrix},$ find $(AB)^{-1}$.

OR Solve the following system of equations by matrix method :$ x+2y+3z=6, 2x-y+z=2, 3x+2y-2z=3.$
HARD
2 Competency APPLY LA 5 Mark(s) 2023
#891
If $A=\begin{bmatrix}3 & 2\\ 5 & -7\end{bmatrix}$, then find $A^{-1}$ and use it to solve the following system of equations : $3x+5y=11, 2x-7y=-3$.
HARD
3 Knowledge APPLY LA 5 Mark(s) 2023
#890
If $A=\begin{bmatrix}1 & 0 & 2\\ 0 & 2 & 1\\ 2 & 0 & 3\end{bmatrix}$, then show that $A^{3}-6A^{2}+7A+2I=O$
MEDIUM
4 Competency APPLY LA 5 Mark(s) 2023
#889
32. Find the inverse of the matrix $A=\begin{bmatrix}1 & -1 & 2\\ 0 & 2 & -3\\ 3 & -2 & 4\end{bmatrix}$. Using the inverse, solve the system of linear equations $x-y+2z=1; 2y-3z=1; 3x-2y+4z=3$.
HARD

Case Study & Passage Based

Read the following passage:
Three students, Neha, Rani and Sam go to a market to purchase stationery items. Neha buys 4 pens, 3 notepads and 2 erasers and pays ₹ 60. Rani buys 2 pens, 4 notepads and 6 erasers for ₹ 90. Sam pays ₹ 70 for 6 pens, 2 notepads and 3 erasers.
1 Competency APPLY SUBJECTIVE 4 Mark(s) 2025 AISSCE(Board Exam)
#972
(i) Form the equations required to solve the problem of finding the price of each item, and express it in the matrix form $AX = B$.
(ii) Find $|A|$ and confirm if it is possible to find $A^{-1}$.
(iii) (a) Find $A^{-1}$, if possible, and write the formula to find $X$.
OR
(iii) (b) Find $A^2 - 8I$, where $I$ is an identity matrix.
EASY