A matrix P has an inverse ${{P}^{-1}}=\left( \begin{matrix} 1 & -3 \\ 0 & 1 \\\end{matrix} \right)$find P
$\left( \begin{matrix} -1 & 3 \\ 0 & -1 \\\end{matrix} \right)$
\[\left( \begin{matrix} 1 & 3 \\ 0 & -1 \\\end{matrix} \right)\]
\[\left( \begin{matrix} 1 & -3 \\ 0 & -1 \\\end{matrix} \right)\]
\[\left( \begin{matrix} 1 & 3 \\ 0 & 1 \\\end{matrix} \right)\]
$\begin{align} & \mathbf{NOTE}:\text{ The product of a matrix and its inverse will only given an identity matrix i}.\text{e }I. \\ & \text{Also if}~\text{Matrix }A=\left( \begin{matrix} a & b \\ c & d \\\end{matrix} \right)\text{ }~\text{its inverse will be given as }{{A}^{-1}}=\frac{1}{ad-bc}\left( \begin{matrix} d & -b \\ -c & a \\\end{matrix} \right) \\ & \text{Given }{{P}^{-1}}=\left( \begin{matrix} 1 & -3 \\ 0 & 1 \\\end{matrix} \right) \\ & P=\frac{1}{(1\times 1)-[0\times (-3)]}\left( \begin{matrix} 1 & 3 \\ 0 & 1 \\\end{matrix} \right)=\frac{1}{1}\left( \begin{matrix} 1 & 3 \\ 0 & 1 \\\end{matrix} \right) \\ & P=\left( \begin{matrix} 1 & 3 \\ 0 & 1 \\\end{matrix} \right) \\\end{align}$