If A is symmetric and B is skew symmetric matrix and $A+B=\begin{bmatrix} 1 & -1\\3 &  2\end{bmatrix}$, then matrix A = _______.

$\begin{bmatrix} 1 & 1\\1 &  2\end{bmatrix}$

The correct answer is Option (3) → $\begin{bmatrix} 1 & 1\\1 &  2\end{bmatrix}$

$A=\begin{bmatrix} a & c\\c &  d\end{bmatrix},B=\begin{bmatrix} 0 & x\\-x &  0\end{bmatrix}$

$A+B=\begin{bmatrix} a+0 & c+x\\c-x &  d+0\end{bmatrix}=\begin{bmatrix} 1 & -1\\3 &  2\end{bmatrix}$

$a=1,c+x=3,d=2,c-x=-1$

$c+x=3$   ...(1)

$c-x=-1$   ...(2)

from (1) and (2)

$2c=2$

$c=1,x=2$

$A=\begin{bmatrix} 1 & 1\\1 &  2\end{bmatrix}$