Answer
$\begin{bmatrix} -2 & -5 \\ -3 & -8 \end{bmatrix}$
Work Step by Step
Let $A= \begin{bmatrix} -8 & 5 \\ 3 & -2 \end{bmatrix}$, do row operations, we have :
$AI= \begin{bmatrix} -8 & 5 \\ 3 & -2 \end{bmatrix}\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}\begin{array} .\\3R1+8R2\to R2\\ \end{array}$
$= \begin{bmatrix} -8 & 5 \\ 0 & -1 \end{bmatrix}\begin{bmatrix} 1 & 0 \\ 3 & 8 \end{bmatrix}\begin{array} .R1+5R2\to R1\\.\\ \end{array}$
$= \begin{bmatrix} -8 & 0 \\ 0 & -1 \end{bmatrix}\begin{bmatrix} 16 & 40 \\ 3 & 8 \end{bmatrix}\begin{array} .R1/(-8)\to R1\\-R2\to R2\\ \end{array}$
$= \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}\begin{bmatrix} -2 & -5 \\ -3 & -8 \end{bmatrix}$
Thus $A^{-1}= \begin{bmatrix} -2 & -5 \\ -3 & -8 \end{bmatrix}$
