Chapter 2 - Matrices - 2.3 The Inverse of a Matrix - 2.3 Exercises - Page 71: 10

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

Let the matrix $A$ be given by $$A=\left[\begin{array}{ccc}{1} &{-2} \\{2}& {-3} \end{array}\right].$$ Since $ad-bc=-3+4=1\neq 0$, then $A$ has inverse given by $$A^{-1}=\left[\begin{array}{ccc}{-3} &{2} \\{-2}& {1} \end{array}\right].$$$