If A and B are symmetric matrices of the same order then (AB – BA) is always

Question

Philoid · Accepted Answer

Given A and B are symmetric matrices

A’ = A --- 1

B’ = B ---- 2

Now (AB – BA)’ = (AB)’ – (BA)’

=B’A’ – A’B’

[’ = B’A’ ]

= BA – AB [Using 1 and 2]

(AB – BA)’ = - (AB - BA)

AB-BA is a skew symmetric matrix.