If $A$ and $B$ are symmetric matrices,prove that $AB - BA$ is a skew-symmetric matrix.

(N/A) Given that $A$ and $B$ are symmetric matrices,we have:
$A' = A$ and $B' = B$ ........ $(1)$
We need to check the transpose of $(AB - BA)$:
$(AB - BA)' = (AB)' - (BA)'$
$= B'A' - A'B'$
$= BA - AB$ (Using equation $(1)$)
$= -(AB - BA)$
Since $(AB - BA)' = -(AB - BA)$,it follows that $(AB - BA)$ is a skew-symmetric matrix.