Chapter 2 - Matrices - 2.3 The Inverse of a Matrix - 2.3 Exercises - Page 71: 34

$$A^{-1}=\frac{1}{9}\left[ \begin {array}{cccccc} - 2&-3\\ -5&-12\end {array} \right].$$

Since $ad-bc=(-12)(-2)-(5)(3)=24-15=9\neq 0$, then $A$ has inverse given by $$A^{-1}=\frac{1}{9}\left[ \begin {array}{cccccc} - 2&-3\\ -5&-12\end {array} \right].$$