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Question
If A and B are symmetric matrices of the same order, then AB – BA is ______.
Options
Skew – symmetric matrix
Symmetric matrix
Diagonal matrix
Identity matrix
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Solution
If A and B are symmetric matrices of the same order, then AB – BA is skew – symmetric matrix.
Explanation:
Given that A and B are symmetric matrices,
A = A’ and B = B’
Then (AB – BA)’ = (AB)’ – (BA)’
= B’A’ – A’B’ ...[∵ A = A’, B = B’]
= BA – AB
= – (AB – BA)
Thus, it is skew – symmetric.
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