If matrix $A=\left[\begin{array}{ll}3 & x \\ y & 0\end{array}\right]$ and A' = A, then :

x = y

$A=\left[\begin{array}{ll}3 & x \\ y & 0\end{array}\right]$

given A' = A

$A'=\left[\begin{array}{ll}3 & 0 \\ x & y\end{array}\right]$

interchange rows with columns

$\Rightarrow \left[\begin{array}{ll}3 & x \\ y & 0\end{array}\right]=\left[\begin{array}{ll}3 & y \\ x & 0\end{array}\right]$

So x = y