cofactor expansion

Computing a determinant by summing entries times signed minors along any row or column.

For an $n\times n$ matrix $A$ , deleting row $i$ and column $j$ leaves a minor $M_{ij}$ , and attaching a sign gives the cofactor $C_{ij}=(-1)^{i+j}M_{ij}$ . Cofactor expansion along any row or column, $\det A = \sum_j a_{ij}C_{ij}$ , always produces the same number — $2n$ different expansions for an $n\times n$ matrix, all equal. A row or column loaded with zeros makes the fastest expansion choice.