Question

If $A=\left[\begin{array}{cc}3& x-1\\ 2x+3& x+2\end{array}\right]$ is symmetric matrix then the value of $x$ is

• A. $4$
• B. $3$
• C. $-4$
• D. $-3$

Answer 1

The correct option is C $-4$

Since $A$ is symmetric matrix, then
$A=A^{\prime }$
$\Rightarrow$ $\left[\begin{array}{cc}3& x-1\\ 2x+3& x+2\end{array}\right]=\left[\begin{array}{cc}3& 2x+3\\ x-1& x+2\end{array}\right]$
$\Rightarrow$ $x-1=2x+3$ $\Rightarrow$ $x=-4$