$\text{If } \Delta = \begin{vmatrix} a_{11}&a_{12}&a_{13} \\ a_{21}&a_{22}&a_{23} \\ a_{31}&a_{32}&a_{33} \end{vmatrix} \text{ and } A_y \text{ is Cofactor of } a_y \text{, then the value of } a_{11}A_{21}+a_{12}A_{22}+a_{13}A_{23}=?$

Question

$\begin{array}{1 1} Hence \bigtriangleup=a_{11}A_{31}+a_{12}A_{32}+a_{13}A_{33} \\Hence \bigtriangleup=a_{11}A_{11}+a_{12}A_{21}+a_{313}A_{31} \\ Hence \bigtriangleup=a_{21}A_{11}+a_{22}A_{21}+a_{23}A_{31} \\ Hence \bigtriangleup=a_{11}A_{11}+a_{21}A_{21}+a_{31}A_{31} \end{array}$