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

[1 mark]

The correct option is B $-4$
$A=\left[\begin{array}{cc}3& x-1\\ 2x+3& x+2\end{array}\right]$
We know that if a matrix is symmetric, then $A^T=A.$
$\Rightarrow \left[\begin{array}{cc}3& 2x+3\\ x-1& x+2\end{array}\right]=\left[\begin{array}{cc}3& x-1\\ 2x+3& x+2\end{array}\right]$

And we know that corresponding entries of equal matrices are equal.
$\Rightarrow x-1=2x+3$
$\therefore x=-4$