Let $A=\left[ {{a}_{ij}} \right]$ be a square matrix of order n. The adjoint of a matrix A is the transporse of the cofactor matrix of A. It is denoted by adj A.

Given $\mathrm{A}=\left[\begin{array}{ll}-1 & 5 \\ -3 & 2\end{array}\right]$
$|A|=\left[\begin{array}{ll}-1 & 5 \\ -3 & 2\end{array}\right]=13 \neq 0$

Since determinant of the matrix is not zero, so inverse of this matrix is possible.

As we know, formula to find matrix inverse is:

$\mathrm{A}^{-1}=\frac{1}{|\mathrm{~A}|} \mathrm{adj} \cdot \mathrm{A}$
adj. $A=\left[\begin{array}{ll}2 & -5 \\ 3 & -1\end{array}\right]$

This implies,

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