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Question
If A and B are symmetric matrices, then AB – BA is a ______.
Solution
If A and B are symmetric matrices, then AB – BA is a skew-symmetric matrix.
Explanation:
Let P = (AB – BA)
P' = (AB – BA)'
= (AB)' – (BA)'
= B'A' – A'B'' ......[∵ (AB)' = B'A']
= BA – AB ......[∵ A' = A and B' = B]
= –(AB – BA)
= –P
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