$\begin{align}  & \text{for a 2}\times \text{2 matrix }A=\left( \begin{matrix}   a & b  \\   c & d  \\\end{matrix} \right) \\ & {{A}^{-1}}=\frac{1}{ad-cd}\left( \begin{matrix}   d & -b  \\   -c & a  \\\end{matrix} \right) \\ & \therefore {{P}^{-1}}=\frac{1}{2+3}\left( \begin{matrix}   1 & 3  \\   -1 & 2  \\\end{matrix} \right)=\tfrac{1}{5}\left( \begin{matrix}   1 & 3  \\   -1 & 2  \\\end{matrix} \right)=\left( \begin{matrix}   \tfrac{1}{5} & \tfrac{3}{5}  \\   \tfrac{-1}{5} & \tfrac{2}{5}  \\\end{matrix} \right) \\\end{align}$