The sum of the products of the elements of any row of a matrix A with the corresponding cofactors of the elements of the same row is always equal to

$|A|$

Let $A =[a_{ij}]$ be a square matrix of order n, then the sum of the product of elements of any row (column) with their cofactors is always equal to $|A|$ or, $det (A)$.

i.e. $\sum\limits_{j=1}^{n}a_{ij}C_{ij} = |A|$ and $\sum\limits_{i=1}^{n}a_{ij}C_{ij} = |A|$