Find the cofactors of the elements for the matrix [ ll -1 & 2 -3 … - Vidyadip

Question

Find the cofactors of the elements for the matrix $\left[\begin{array}{ll}-1 & 2 \\ -3 & 4\end{array}\right]$

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Answer

Let $A=\left[\begin{array}{ll}-1 & 2 \\ -3 & 4\end{array}\right]=\left[\begin{array}{ll}a_{11} & a_{12} \\ a_{21} & a_{22}\end{array}\right]$
Here,
$A_{11}=(-1)^2(4)=4=\text { cofactor of } a_{11}$
$A_{12}=(-1)^3(-3)=3=\text { cofactor of } a_{12}$
$A_{21}=(-1)^3(2)=-2=\text { cofactor of } a_{21}$
$A_{22}=(-1)^4(-1)=-1=\text { cofactor of } a_{22}$
Hence cofactors are
$A_{11}=4, A_{12}=3$
$A_{21}=-2, A_{22}=-1$

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