Find the adjoint of the following matrices : [ cc 2 & -3 3 & 5 ] - Vidyadip

Question

Find the adjoint of the following matrices $:\left[\begin{array}{cc}2 & -3 \\ 3 & 5\end{array}\right]$

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Answer

Let $A=2 -3$
Here, $a_{11}=2, M_{11}=5$
$\therefore A_{11}=(-1)^{1+1}(5)=5$
$a_{12}=-3, M_{12}=3$
$\therefore A_{12}=(-1)^{1+2}(3)=-3$
$a_{21}=3, M_{21}=-3$
$\therefore A A_{21}=(-1)^{2+1}(-3)=3$
$a_{22}=5, M_{22}=2$
$\therefore A_{22}=(-1)^{2+1}=2$
$\therefore$ the co$-$factor matrix $=\left[\begin{array}{ll}A_{11} & A_{12} \\ A_{21} & A_{22}\end{array}\right]$
$ =\left[\begin{array}{rr}5 & -3 \\ 3 & 2\end{array}\right] $
$ \therefore \operatorname{adj~} \mathrm{A}=\left(\begin{array}{rr}5 & 3 \\ -3 & 2\end{array}\right)$

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