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Calculate the inverse of any square invertible matrix using Gauss-Jordan elimination. [A|I] → [I|A⁻¹]. 100% client-side—no data sent to servers. Supports 2×2 to 6×6.
The inverse A⁻¹ satisfies A × A⁻¹ = I. This tool uses Gauss-Jordan elimination on [A|I] to produce [I|A⁻¹]. A matrix is singular (no inverse) when det(A)=0. All calculations run client-side—no data stored.
Enter your square matrix and click Calculate. The tool performs Gauss-Jordan elimination on the augmented matrix [A | I] until it reaches [I | A⁻¹]. If det(A) = 0 at any point, the matrix is singular and has no inverse.
A matrix is non-invertible (singular) when det(A) = 0. This typically happens when rows or columns are linearly dependent, or rank(A) < n for an n×n matrix.
This calculator supports 2×2 up to 6×6 matrices. It includes optional verification that A × A⁻¹ = I, and shows intermediate Gauss-Jordan steps.
A square matrix has no inverse when its determinant is zero (singular). This happens when rows are linearly dependent, the matrix has a zero row/column, or rank(A) < n. Non-square matrices never have a standard inverse.