Matrix Inverse Calculator

Calculate the inverse of any square matrix up to 5x5.

Matrix Size

Enter Matrix A

Adjugate Matrix (adj A)

-24.00

18.00

5.00

20.00

-15.00

-4.00

-5.00

4.00

1.00

Determinant

1.000000

Matrix is invertible

Inverse Matrix (A^-1)

-24.0000

18.0000

5.0000

20.0000

-15.0000

-4.0000

-5.0000

4.0000

1.0000

Formula

A^-1 = (1/det(A)) * adj(A)

The inverse is calculated by multiplying the adjugate matrix by 1/determinant.

Properties of Inverse

A * A^-1 = I (identity matrix)
(AB)^-1 = B^-1 * A^-1
(A^-1)^-1 = A
(A^T)^-1 = (A^-1)^T
det(A^-1) = 1/det(A)