If $A=\left[a_{i j} ight]_{3 imes 3}=\left[\begin{array}{ccc}1 & 3 & 3 \ -1 & 2 & 2 \ 1 & 1 & 4\end{array} ight]$ and $A_{i j}$ is a cofactor of $a_{i j}$ then the value of $a_{31} A_{31}+a_{32} A_{32}+a_{33} A_{33}$ is equal to

Question

If $A=\left[a_{i j}ight]_{3 	imes 3}=\left[\begin{array}{ccc}1 & 3 & 3 \ -1 & 2 & 2 \ 1 & 1 & 4\end{array}ight]$ and $A_{i j}$ is a cofactor of $a_{i j}$ then the value of $a_{31} A_{31}+a_{32} A_{32}+a_{33} A_{33}$ is equal to

Aicharya · Accepted Answer

$\begin{aligned} & a_{31} A_{31}+a_{32} A_{32}+a_{33} A_{33}=|A| \ & =1 	imes(8-2)-3(-4-2)+3(-1-2)=6+18-9=15\end{aligned}$

If $A=\left[a_{i j}\right]_{3 \times 3}=\left[\begin{array}{ccc}1 & 3 & 3 \\ -1 & 2 & 2 \\ 1 & 1 &…

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