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.