Answer
$\begin{bmatrix}
-\frac{2}{b}&\frac{3}{b}\\
1&-1
\end{bmatrix}$
Work Step by Step
Using the formula,
$A^{-1} = \frac{1}{|A|}\times{Adj(A)}$
$where, A = \begin{bmatrix} b&3\\b&2\end{bmatrix}$
$Adj(A) = \begin{bmatrix}d&-b\\-c&a\end{bmatrix}, if A = \begin{bmatrix}a&b\\c&d\end{bmatrix}$
$\implies A^{-1} = \frac{1}{2b-3b}\times\begin{bmatrix}2&-3\\-b&b\end{bmatrix}$
$\quad = \frac{1}{-b}\times\begin{bmatrix}2&-3\\-b&b\end{bmatrix} = \begin{bmatrix}-\frac{2}{b}&\frac{3}{b}\\1&-1\end{bmatrix}$
