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If $\mathrm{A}=\left[\mathrm{a}_{\mathrm{ij}}\right]_{3 \times 3}=\left[\begin{array}{lll}1 & 2 & 3 \\ 1 & 1 & 5 \\ 2 & 4 & 7\end{array}\right]$ and $\mathrm{Aij}$ is a cofactor of $\mathrm{a}_{\mathrm{ij}}$, then $a_{11} A_{21}+a_{12} A_{22}+a_{13} A_{23}$ is equal to
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The correct answer is:
$0$
If we multiply elements of one row to the corresponding cofactors of another row and add them then we get zero hence,
$a_{11} A_{21}+a_{12} A_{22}+a_{13} A_{23}=0$
$a_{11} A_{21}+a_{12} A_{22}+a_{13} A_{23}=0$
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