InterviewSolution
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InterviewSolution
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Show that a matrix which is both symmetric and skew symmetric is a zero matrix. |
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Answer» Let A = [aij] be a matrix which is both symmetric and skew symmetric. Since A is a skew symmetric matrix, so A′ = –A. Thus for all i and j, we have aij = – aji. .........(1) Again, since A is a symmetric matrix, so A′ = A. Thus, for all i and j, we have aji = aij .............(2) Therefore, from (1) and (2), we get aij = –aij for all i and j or 2aij = 0, i.e., aij = 0 for all i and j. Hence A is a zero matrix. |
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