If $S=\begin{bmatrix}a&b\\c&d\end{bmatrix}$, then adj A is equal to

$\begin{bmatrix}-d&-b\\-c&a\end{bmatrix}$ $\begin{bmatrix}d&-b\\-c&a\end{bmatrix}$ $\begin{bmatrix}d&-b\\c&a\end{bmatrix}$ $\begin{bmatrix}d&c\\b&a\end{bmatrix}$

$\begin{bmatrix}d&-b\\-c&a\end{bmatrix}$

We have, $C_{11}$ = Cofactor of a in $S=d$, $C_{12}$ = Cofactor of b in $S=-c$ $C_{21}$ = Cofactor of c in $S=-b$, $C_{22}$= Cofactor of d in $S = a$ $∴adj\,S=\begin{bmatrix}a&-b\\-c&d\end{bmatrix}^T=\begin{bmatrix}d&-b\\-c&a\end{bmatrix}$