Chapter 2 - Matrices - 2.3 The Inverse of a Matrix - 2.3 Exercises - Page 71: 9

$$A^{-1}= \left[\begin{array}{ccc}{7} &{-2} \\{-3}& {1} \end{array}\right].$$

Let the matrix $A$ be given by $$A=\left[\begin{array}{ccc}{1} &{2} \\{3}& {7} \end{array}\right].$$ Since $ad-bc=7-6=1\neq 0$, then $A$ has inverse given by $$A^{-1}= \left[\begin{array}{ccc}{7} &{-2} \\{-3}& {1} \end{array}\right].$$