Find the adjoint of matrix A= [ cc 2 & -3 4 & 1 ]

Question

Find the adjoint of matrix $A=\left[\begin{array}{cc}2 & -3 \\ 4 & 1\end{array}\right]$

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Answer

$\therefore M_{11}=1$
$\therefore A_{11}=(-1)^{1+1}(1)=1$
$\therefore M_{12}=4$
$\therefore A_{12}=(-1)^{1+2}(4)=-4$
$\therefore M_{21}=-3$
$\therefore A_{21}=(-1)^{2+1}(-3)=3$
$\therefore M_{22}=2$
$\therefore A_{22}=(-1)^{2+2}(2)=2$
Here $a_{11}=2$
$a _{12}=-3$
$a_{21}=4$
$a_{22}=1$
$\therefore \quad \text { the matrix }\left[A_{i i}\right]_{ D 2}=\left[\begin{array}{cc} 1 & 4 \\ 3 & 2\end{array}\right]$
$\therefore \quad\left[A_{i j}\right]_{2 \infty 2}^{ T }=\left[\begin{array}{cc} 1 & 3 \\ -4 & 2\end{array}\right]$
$\therefore \quad \text { adj } A \quad=\left[\begin{array}{cc} 1 & 3 \\ -4 & 2\end{array}\right]$

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