Chapter 2 - Matrices - 2.3 The Inverse of a Matrix - 2.3 Exercises - Page 71: 32

$$A^{-1}=-\frac{1}{4}\left[ \begin {array}{cccccc} 2&2\\ 3&1\end {array} \right].$$

Since $ad-bc=(1)(2)-(-2)(-3)=2-6=-4\neq 0$, then $A$ has inverse given by $$A^{-1}=-\frac{1}{4}\left[ \begin {array}{cccccc} 2&2\\ 3&1\end {array} \right].$$