Mathematics - Matrices Question with Solution | TestHub

A square matrix $P$ is said to be a symmetric matrix, if $P^T=P$ and it is said to be a skew symmetric matrix, if $P^T=-P.$

Given $A^T=A, B^T=-B$

Now, ${\left(AB-BA\right)}^T={\left(AB\right)}^T-{\left(BA\right)}^T$

                    $=B^T{A}^T-A^T{B}^T$

                    $=(-B)A-A(-B)$

                    $=AB-BA$

$\Rightarrow AB-BA$ is a symmetric matrix.