Work out cofactor matrix instantly with clear inputs, formula shown and shareable results.
The minor Mᵢⱼ is the determinant of the matrix with row i and column j deleted. The cofactor attaches the chequerboard sign (−1)^(i+j), and cofactors are what make Laplace expansion and the adjugate work.
Cofactor
Cᵢⱼ = (−1)^(i+j) · Mᵢⱼ
A cofactor is the minor multiplied by (−1)^(i+j), so they differ only by sign — and agree whenever i + j is even.
It keeps Laplace expansion consistent with the determinant's behaviour under row swaps, each of which flips the sign.