Solve this

$A \times B=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$

$A \times B$ is a non $-$ singular matrix. Therefore, it is invertible.

Let $C_{i j}$ be a cofactor of $a_{i j}$ in $A$.

The cofactors of element $A$ are given by

$C_{11}=d$

$C_{12}=-c$

$C_{21}=-b$

$C_{22}=a$

$\therefore \operatorname{adj} A=\left[\begin{array}{cc}d & -c \\ -b & a\end{array}\right]^{T}=\left[\begin{array}{cc}d & -b \\ -c & a\end{array}\right]$