The inverse of the matrix $\begin{bmatrix}5 & 11\\1 & 2\end{bmatrix}$ is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $\begin{bmatrix}-2 & 11\\1 & -5\end{bmatrix}$
$A=\begin{bmatrix}5 & 11\\1 & 2\end{bmatrix}$
$|A|=10-11=-1$
$adj\,A=\begin{bmatrix}2 & -11\\-1 & 5\end{bmatrix}⇒A^{-1}=\frac{adj\,A}{|A|}=(-1)\begin{bmatrix}2 & -11\\-1 & 5\end{bmatrix}$
$=\begin{bmatrix}-2 & 11\\1 & -5\end{bmatrix}$