Solve this

$|A|=\left|\begin{array}{cc}1 & -3 \\ 2 & 0\end{array}\right|=6 \neq 0$

$A$ is a non-singular matrix. Therefore, it is invertible.

Let $C_{i j}$ be a cofactor of $a_{i j}$ in $A$.

The cofactors of element $A$ are given by

$C_{11}=0$

$C_{12}=-2$

$C_{21}=3$

$C_{22}=1$

$\therefore \operatorname{adj} A=\left[\begin{array}{cc}0 & -2 \\ 3 & 1\end{array}\right]^{T}=\left[\begin{array}{cc}0 & 3 \\ -2 & 1\end{array}\right]$