Answer
$$A^{-1}=\frac{1}{13}\left[ \begin {array}{cccccc} 5&-3\\
1&2\end {array} \right].$$
Work Step by Step
Since $ad-bc=(2)(5)-(-1)(3)=10+3=13\neq 0$, then $A$ has inverse given by
$$A^{-1}=\frac{1}{13}\left[ \begin {array}{cccccc} 5&-3\\
1&2\end {array} \right].$$