If A is a symmetric matrix and B is skew- symmetric matrix such...

Given $A$ is symmetric and $B$ is skew symmetric, hence
A = \left[\begin{cases}a & b \\ b & c\end{cases}\right] and B = \left[\begin{cases}0 & d \\ - d & 0\end{cases}\right]
Now A + B = \left[\begin{cases}a & b + d \\ b - d & c\end{cases}\right] = \left[\begin{cases}2 & 3 \\ 5 & - 1\end{cases}\right]
$⇒ a = 2, b = 4, c = - 1$ and $d = - 1$
⇒ A = \left[\begin{cases}2 & 4 \\ 4 & - 1\end{cases}\right] and B = \left[\begin{cases}0 & - 1 \\ 1 & 0\end{cases}\right]
Hence AB = \left[\begin{cases}2 & 4 \\ 4 & - 1\end{cases}\right]\left[\begin{cases}0 & - 1 \\ 1 & 0\end{cases}\right] = \left[\begin{cases}4 & - 2 \\ - 1 & - 4\end{cases}\right]