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A symmetric matrix is a square matrix that is equal to its transpose (A = AT).
A skew-symmetric matrix is a square matrix whose transpose is equal to its negative (AT = -A).
Let's consider a matrix that is both symmetric and skew-symmetric. If A is both, then A = AT and AT = -A. Therefore, A = -A.
This implies that all elements of A must be zero (aij = -aij, which means aij = 0 for all i and j).
Therefore, the matrix must be a null matrix.
Correct Answer: Null Matrix