Find the inverse of a square matrix quickly and accurately. Enter your matrix values, choose the matrix size, and calculate the inverse with an easy-to-read result.
Select the matrix size and enter the values in each cell.
The inverse of a square matrix is another matrix that, when multiplied by the original matrix, produces the identity matrix.
If A is a square matrix and its inverse is A⁻¹, then:
A × A⁻¹ = A⁻¹ × A = I
A matrix has an inverse only when its determinant is non-zero.
A matrix with a determinant of zero does not have an ordinary inverse.
For an invertible square matrix A, the inverse can be expressed using the determinant and adjugate matrix:
A⁻¹ = 1 / det(A) × adj(A)
For a 2 × 2 matrix, the inverse can be found using the determinant and the following standard formula:
A = [ a b ]
[ c d ]
det(A) = ad − bc
A⁻¹ = 1/(ad − bc) [ d −b ]
[ −c a ]
If the determinant is zero, the matrix is singular and its ordinary inverse does not exist.
This calculator is designed to make matrix inverse calculations faster and easier for students, teachers, engineers, and anyone working with linear algebra.
Matrix inverses are an important part of linear algebra and are used in many mathematical and technical applications.