Question
If A, B are symmetric matrices of the same order then (AB – BA) is -
- symmetric matrix
- skew-symmetric matrix
- null matrix
- unit matrix
The correct answer is: skew-symmetric matrix
A' = A & B' = B given
(AB – BA)' = (AB)' – (BA)'
= B'.A' – A'.B'
= B. A – A. B
= – (AB – BA)
AB – BA is skew symmetric matrix
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