Solve this


If $A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right], B=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$, find adj $(A B)$


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

$A \times B$ 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





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

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