What is the Inverse Matrix Calculator?
Find the inverse of a square matrix up to 6×6 using Gauss–Jordan elimination. Enter matrix A and get A⁻¹, det(A), elimination steps, and a verification that A × A⁻¹ ≈ I. Singular matrices (det = 0) are reported with a clear error. Free, private, and instant in your browser.
How to use the Inverse Matrix Calculator
- Choose the matrix size n (n×n).
- Enter values for matrix A in the grid.
- Read A⁻¹, det(A), and the verification note.
- Review Gauss–Jordan steps and the A × A⁻¹ check.
- Copy the full result.
Common use cases
- Finding A⁻¹ for a 2×2 or 3×3 homework problem
- Checking invertibility before solving a linear system
- Verifying inverse calculations with A × A⁻¹ ≈ I
Frequently asked questions
- When does a matrix have no inverse?
- Only square matrices can be inverted, and only when det(A) ≠ 0. If det(A) = 0 the matrix is singular.
- What method is used?
- Gauss–Jordan elimination on the augmented matrix [A | I] to produce [I | A⁻¹].
- What is the verification step?
- The calculator multiplies A × A⁻¹ and checks that the result is approximately the identity matrix I.
- What matrix sizes are supported?
- Square matrices from 1×1 up to 6×6.
