Question:
Write the adjoint of the matrix $A=\left[\begin{array}{cc}-3 & 4 \\ 7 & -2\end{array}\right]$.
Solution:
Let $C_{i j}$ be a cofactor of $a_{i j}$ in $A$.
Now,
$C_{11}=-2$
$C_{12}=-7$
$C_{21}=-4$
$C_{22}=-3$
$\therefore \operatorname{adj} A=\left[\begin{array}{ll}-2 & -7 \\ -4 & -3\end{array}\right]^{T}=\left[\begin{array}{ll}-2 & -4 \\ -7 & -3\end{array}\right]$