If A and B are matrices of same order, then $\left( {A{B^\prime } - B{A^\prime }} \right)$ is A

We have matrices A and B of same order.

Let $P = \left( {A{B^\prime } - B{A^\prime }} \right)$
Then, ${P^\prime } = {\left( {A{B^\prime } - B{A^\prime }} \right)^\prime } = {\left( {A{B^\prime }} \right)^\prime } - {\left( {B{A^\prime }} \right)^\prime }$

$= {\left( {{B^\prime }} \right)^\prime }{(A)^\prime } - {\left( {{A^\prime }} \right)^\prime }{B^\prime } = B{A^\prime } - A{B^\prime }$

$= - \left( {A{B^\prime } - B{A^\prime }} \right) = - P$
Hence, $\left( {A{B^\prime } - B{A^\prime }} \right)$ is a skew-symmetric matrix.