Write the adjoint of the matrix

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,

$C_{11}=-2$

$C_{12}=-7$

$C_{21}=-4$

$C_{22}=-3$

$\therefore \operatorname{adj} A=\left[\begin{array}{ll}-2 & -7 \\ -4 & -3\end{array}\right]^{T}=\left[\begin{array}{ll}-2 & -4 \\ -7 & -3\end{array}\right]$

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