Answer
$$A^{-1}=\frac{20}{59}\left[ \begin {array}{cccccc} \frac{4}{5}&\frac{3}{4}\\ -\frac{1}{5}&\frac{7}{2}\end {array} \right].$$
Work Step by Step
Since $ad-bc=\frac{7}{2}\frac{4}{5}+\frac{3}{4}\frac{1}{5}=\frac{59}{20}\neq 0$, then $A$ has inverse given by $$A^{-1}=\frac{20}{59}\left[ \begin {array}{cccccc} \frac{4}{5}&\frac{3}{4}\\ -\frac{1}{5}&\frac{7}{2}\end {array} \right].$$
