Let $A$ and $B$ be nxn matrices and let $A(i|j)$ denote the matrix $A$ obtained by removing the ith row and jth column of $A$. I want to show the cofactor of $AB$ is equal to the cofactor of $A$ times the cofactor of $B$. So I try to show that
$$\sum_k \det(A(i|k)B(k|j))= \det(AB)(i|j),$$ but I don't see why this is true. Can anyone explain?