$\therefore$ $A' = A,B' = B$ Now $\,\,\,\left( {A\left( {BA} \right)} \right)' = \left( {BA} \right)'A'$ $= \left( {A'B'} \right)A' = \left( {AB} \right)A = A\left( {BA} \right)$ Similarly $\left( {\left( {AB} \right)A} \right)' = \left( {AB} \right)A$ So, $A\left( {BA} \right)\,\,\,\,$ and $A\left( {BA} \right)\,\,\,\,$ are symmetric matrices. Again $\left( {AB} \right)' = B'A' = BA$ Now if $BA=AB$, then $AB$ is symmetric matrix.