Q. 194.9( 7 Votes )

If A and B are symmetric matrices of the same order, show that (AB – BA) is a skew symmetric matrix.

Answer :

We are given that A and B are symmetric matrices of the same order then, we need to show that (AB – BA) is a skew symmetric matrix.


Let us consider P is a matrix of the same order as A and B


And let P = (AB – BA),


we have A = A’ and B = B’


then, P’ = (AB – BA)’


P’ = ((AB)’ – (BA)’) …….using reversal law we have (CD)’=D’C’


P’ = (B’A’ – A’B’)


P’ = (BA – AB)


P’ = -P


Hence, P is a skew symmetric matrix.


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