The inverse of matrix N =$\left( \begin{matrix} 2 & 3 \\ 1 & 4 \\\end{matrix} \right)$ is
$\frac{1}{5}\left( \begin{matrix} 2 & -1 \\ -3 & 4 \\\end{matrix} \right)$
$\frac{1}{5}\left( \begin{matrix} 4 & 3 \\ -1 & 2 \\\end{matrix} \right)$
$\frac{1}{5}\left( \begin{matrix} 4 & -3 \\ -1 & 2 \\\end{matrix} \right)$
$\frac{1}{5}\left( \begin{matrix} 2 & 1 \\ 3 & 4 \\\end{matrix} \right)$
$\begin{align} & \text{For a given 2}\times \text{2 matrix}\,A=\left( \begin{matrix} a & b \\ c & d \\\end{matrix} \right) \\ & the\text{ }inverse\text{ }{{A}^{}}^{1}is\text{ }given\text{ }as \\ & {{A}^{-1}}=\left( \begin{matrix} d & -b \\ -c & a \\\end{matrix} \right) \\ & \therefore N=\left( \begin{matrix} 2 & 3 \\ 1 & 4 \\\end{matrix} \right) \\ & {{N}^{-1}}=\frac{1}{8-3}\left( \begin{matrix} 4 & -3 \\ -1 & 2 \\\end{matrix} \right)=\frac{1}{5}\left( \begin{matrix} 4 & -3 \\ -1 & 2 \\\end{matrix} \right) \\\end{align}$