Find the inverse of the matrix

$|A|=\left|\begin{array}{cc}3 & -2 \\ -7 & 5\end{array}\right|=1 \neq 0$

$A$ 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

$C_{11}=5$

$C_{12}=7$

$C_{21}=2$

$C_{22}=3$

$\therefore A^{-1}=\frac{1}{|A|}\left[\begin{array}{ll}5 & 7 \\ 2 & 3\end{array}\right]^{T}=\left[\begin{array}{ll}5 & 2 \\ 7 & 3\end{array}\right]$