A matrix which is both symmetric as well as skew-symmetric is a nullma – InterviewSolution

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1.	A matrix which is both symmetric as well as skew-symmetric is a nullmatrix.
Answer» A matrix `A` is symmetric if `A = A^T`. `=> a_(ij) = a_(ji),` for all `i,j->(1)` Here `a_(ij)` are elements of matrix with `i` and `j` representing rows and columns of matrix. A matrix `A` is skew-symmetric if `A = -A^T`. `=> a_(ij) = -a_(ji),` for all `i,j` `=>-a_(ij) = a_(ji)->(2)` From (1) and (2), `a_(ij) = -a_(ij)` `=>2a_(ij) = 0` `=>a_(ij) = 0` So, each element of the matrix will be `0`. thus, it will be a null matrix.

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