Question

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

• A. 4
• B. 3
• C. -4
• D. -3

Answer 1

Answer: (C)

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