Find the adjoint of matrix A= [ ll 6 & 5 3 & 4 ] - Vidyadip

Question

Find the adjoint of matrix $A=\left[\begin{array}{ll}6 & 5 \\ 3 & 4\end{array}\right]$

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Answer

$A=\left[\begin{array}{ll}6 & 5 \\ 3 & 4\end{array}\right]$
$A_{11}=(-1)^{1+1} M_{11}=M_{11}=4$
$A_{12}=(-1)^{1+2} M_{12}=-M_{12}=-3$
$A_{21}=(-1)^{2+1} M_{21}=-M_{21}=-5$
$A_{22}=(-1)^{2+2} M_{22}=M_{22}=6$
$\begin{aligned} & \operatorname{adj} A=\left[\begin{array}{ll}A_{11} & A_{12} \\ A_{21} & A_{22}\end{array}\right]^T \\ & =\left[\begin{array}{cc}4 & -3 \\ -5 & 6\end{array}\right]^T \\ & =\left[\begin{array}{cc}4 & -5 \\ -3 & 6\end{array}\right]\end{aligned}$

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