The sum of products of elements of any row with the cofactors of corresponding elements is equal to……………….

The sum of products of elements of any row with the cofactors of corresponding elements is equal to value of the determinant.

Let $\Delta = \left| {\begin{array}{llllllllllllllllllll}{{a_{11}}}&{{a_{12}}}&{{a_{13}}}\\{{a_{21}}}&{{a_{22}}}&{{a_{23}}}\\{{a_{31}}}&{{a_{32}}}&{{a_{33}}}\end{array}} \right|$

Expanding along ${R_1}$,

$\Delta = {a_{11}}{A_{11}} + {a_{12}}{A_{12}} + {a_{13}}{A_{13}}$

$=$ Sum of products of elements of ${R_1}$ with their corresponding cofactors