Let $A=\left[\begin{array}{ccc}3& a& -1\\ 2& 5& c\\ b& 8& 2\end{array}\right]$ is symmetric and $B=\left[\begin{array}{ccc}d& 3& a\\ b-a& e& -2b-c\\ -2& 6& -f\end{array}\right]$ is skew-symmetric, find $AB$. 

$\because A$ is symmetric

$\therefore c=8, b=-1 and a=2 and B$is skew-symmetric       ..(i)

$\therefore d=e=f=0 and 2b+c=6, a=2, b-a=-3$           ..(ii)

From Eqs. (i) and (ii), we get

$a=2, b=-1, c=8, d=0, e=0, f=0$

$\therefore A=\left[\begin{array}{ccc}3& 2& -1\\ 2& 5& 8\\ -1& 8& 2\end{array}\right]$ and $B=\left[\begin{array}{ccc}0& 3& 2\\ -3& 0& -6\\ -2& 6& 0\end{array}\right]$

$\Rightarrow AB=\left[\begin{array}{ccc}-4& 3& -6\\ -31& 54& -26\\ -28& 9& -50\end{array}\right]$