Find the inverse of each of the matrices (if it exists).

Let $A=\left[\begin{array}{ll}-1 & 5 \\ -3 & 2\end{array}\right]$

we have,

$|A|=-2+15=13$

Now,

$A_{11}=2, A_{12}=3, A_{21}=-5, A_{22}=-1$

$\therefore \operatorname{adj} A=\left[\begin{array}{ll}2 & -5 \\ 3 & -1\end{array}\right]$

$\therefore A^{-1}=\frac{1}{|A|}$ adjA $=\frac{1}{13}\left[\begin{array}{ll}2 & -5 \\ 3 & -1\end{array}\right]$