Matrix Inverse Calculator
Calculate the inverse of a square matrix of any size.
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Enter a square matrix to calculate its inverse.
Rows separated by semicolons, entries by commas — e.g. "1,2;3,4" for a 2x2 matrix. Must be square.
Your result
-2, 1; 1.5, -0.5
Inverse matrix
Determinant-2
AI explanation
Formula
Computed via Gauss-Jordan elimination on the matrix augmented with the identity matrixWorked example
Inverse of [[1,2],[3,4]]
| Field | Value |
|---|---|
| Matrix | 1,2;3,4 |
| Inverse matrix | -2, 1; 1.5, -0.5 |
| Determinant | -2 |
Assumptions
- Only a square, non-singular (non-zero determinant) matrix has an inverse — a singular matrix shows an error.
Frequently asked questions
What is a matrix inverse used for?
Solving systems of linear equations (Ax = b becomes x = A⁻¹b), among other applications in linear algebra and computer graphics.
Why do some matrices have no inverse?
A matrix with a determinant of 0 (called "singular") has no inverse — its rows or columns are linearly dependent.
How is the inverse computed for larger matrices?
Via Gauss-Jordan elimination — augmenting the matrix with the identity matrix and row- reducing until the original matrix becomes the identity, leaving the inverse on the augmented side.