Cofactor Matrix Calculator

Determinant

det(A) computed via cofactor expansion along the first row.

Cofactor matrix (encoded)[-12,15,-4,6,-12,6,0,3,-2]

Minors matrix (encoded)[-12,-15,-4,-6,-12,-6,0,-3,-2]

Adjugate matrix (encoded)[-12,6,0,15,-12,3,-4,6,-2]

Matrix size3 x 3

Invertible?Yes

Inverse matrix (encoded)[-2,1,0,2.5,-2,0.5,-0.666667,1,-0.333333]

Determinant6

det(A) = 6 - matrix is invertible

The 3x3 cofactor matrix was computed by replacing each entry with the signed determinant of its submatrix.
The adjugate matrix (transpose of the cofactor matrix) is the key to finding the inverse using adj(A) / det(A).
With det(A) = 6, this matrix is invertible and the inverse has been computed.
Cofactors also appear in Cramer's rule for solving linear systems and in the Leibniz determinant formula.

Next stepUse the inverse A^(-1) shown in the steps to solve Ax = b: multiply both sides by A^(-1).

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