If $A=\begin{bmatrix}a&b\\c&d\end{bmatrix}$ such that $ad - bc ≠ 0$, then $A^{-1}$, is

$\frac{1}{ad-bc}\begin{bmatrix}d&-b\\c&a\end{bmatrix}$ $\frac{1}{ad-bc}\begin{bmatrix}d&b\\-c&a\end{bmatrix}$ $\begin{bmatrix}d&-b\\c&a\end{bmatrix}$ none of these

$\frac{1}{ad-bc}\begin{bmatrix}d&-b\\c&a\end{bmatrix}$

We have, $|A|= ad - bc ≠ 0$ Cofactor of $a_{11}=d$, Cofactor of $a_{12} = -c$ Cofactor of $a_{21}=-b$, Cofactor of $a_{22} = a$ $∴A^{-1}=\frac{1}{|A|}adj\,A=\frac{1}{ad-bc}\begin{bmatrix}d&-b\\-c&a\end{bmatrix}$.