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

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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