Cofactors

Cofactors: The cofactor $C_{ij}$ of entry $a_{ij}$ is $C_{ij} = (-1)^{i+j} M_{ij}$, where $M_{ij}$ is the minor (determinant of the submatrix obtained by deleting row $i$ and column $j$). The determinant can be computed by cofactor expansion along any row or column: $\det(A) = \sum_j a_{ij}C_{ij}$.