If cofactor C _ i j represent for element p_ i j , of matrix P = … - Vidyadip

Question

If cofactor $C _{i j}$ represent for element $p_{i j},$ of matrix $P =\left[\begin{array}{ccc}1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & 2 & 4\end{array}\right]$ then value of $C_{31} . C_{23}$ is $:$

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Answer

$C_{31}=(-1)^{3+1}\left|\begin{array}{cc}-1 & 2 \\ 2 & -3\end{array}\right|=3-4=-1 $
$ C_{23}=(-1)^{2+3}\left|\begin{array}{cc}1 & -1 \\ 3 & 2\end{array}\right|=-(2+3)=-5$
Hence $C_{31} \cdot C_{23}$
$=(-1)(-5)$
$=5$

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