Chapter 2 - Matrices - 2.3 The Inverse of a Matrix - 2.3 Exercises - Page 71: 7

$$A^{-1}=\frac{1}{6}\left[\begin{array}{ccc}{3} &{0} \\{0}& {2} \end{array}\right].$$

Let the matrix $A$ be given by $$A=\left[\begin{array}{ccc}{2} &{0} \\{0}& {3} \end{array}\right].$$ Since $ad-bc=6-0=6\neq 0$, then $A$ has inverse given by $$A^{-1}=\frac{1}{6}\left[\begin{array}{ccc}{3} &{0} \\{0}& {2} \end{array}\right].$$