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cofactor

A minor with a checkerboard sign attached: $C_{ij}=(-1)^{i+j}M_{ij}$ .

The cofactor $C_{ij}=(-1)^{i+j}M_{ij}$ attaches a checkerboard sign — starting with $+$ in the top-left corner — to the minor $M_{ij}$ . Cofactor expansion sums entries times their cofactors to compute a determinant.