Cofactor Expansion Calculator

Your details

Choose the order of your square matrix.
Enter all entries left-to-right, top-to-bottom, separated by commas. For a 3x3 matrix enter 9 numbers; for a 4x4 enter 16.
Choose any row or column. The determinant is the same no matter which you pick (Laplace theorem). Pick the one with the most zeros to minimize arithmetic.
DeterminantInvertible (non-singular)
10

det(A) computed via cofactor expansion

Invertible?Yes (det != 0)
Expansion formula(+1)(2)(10) + (-1)(-1)(2) + (+1)(3)(4) = 10
Cofactor matrix C[[10, -2, -4], [10, -1, -7], [-10, 4, 8]]
Adjugate (adj A)[[10, 10, -10], [-2, -1, 4], [-4, -7, 8]]
Determinant10

Determinant = 10 - the matrix is invertible.

  • The determinant is 10, which is non-zero, so the matrix is invertible.
  • The inverse can be found as A⁻¹ = adj(A) / 10, using the adjugate shown below.
  • For a 3x3 matrix, cofactor expansion reduces the problem to three 2x2 determinants, each weighted by its sign and entry value.

Next stepTo find the inverse, divide each entry of the adjugate matrix by the determinant.

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