The inverse of the matrix $\begin{bmatrix}5 & 11\\1 & 2\end{bmatrix}$ is :

$\begin{bmatrix}-2 & 11\\1 & -5\end{bmatrix}$

The correct answer is Option (1) → $\begin{bmatrix}-2 & 11\\1 & -5\end{bmatrix}$

$A=\begin{bmatrix}5 & 11\\1 & 2\end{bmatrix}$

$|A|=10-11=-1$

$adj\,A=\begin{bmatrix}2 & -11\\-1 & 5\end{bmatrix}⇒A^{-1}=\frac{adj\,A}{|A|}=(-1)\begin{bmatrix}2 & -11\\-1 & 5\end{bmatrix}$

$=\begin{bmatrix}-2 & 11\\1 & -5\end{bmatrix}$