If $\mathrm{a}$ is $\mathrm{A}$ symmetric matrix and $\mathrm{B}$ is a skewsymmetrix matrix such that $\mathrm{A}+\mathrm{B}=\left[\begin{array}{cc}2 & 3 \\ 5 & -1\end{array}\right]$, then $\mathrm{AB}$ is equal to :
Correct Option: , 3
$\mathrm{A}=\mathrm{A}^{\prime}, \mathrm{B}=-\mathrm{B}^{\prime}$
$\mathrm{A}+\mathrm{B}=\left[\begin{array}{cc}2 & 3 \\ 5 & -1\end{array}\right]$ ...........(1)
$\mathrm{A}^{\prime}+\mathrm{B}^{\prime}=\left[\begin{array}{cc}2 & 5 \\ 3 & -1\end{array}\right]$
$A-B=\left[\begin{array}{cc}2 & 5 \\ 3 & -1\end{array}\right]$ .............(2)
After adding Eq. (1) & (2)
$A=\left[\begin{array}{cc}2 & 4 \\ 4 & -1\end{array}\right], \quad B=\left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right]$
$\mathrm{AB}=\left[\begin{array}{cc}4 & -2 \\ -1 & -4\end{array}\right]$