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Academic / Student Tools / Matrix Inverse Calculator
Tool 468 · exact inverse lab

Invert the matrix — and verify every step.

Enter integers, decimals or fractions. Exact rational Gauss–Jordan elimination is used throughout, with row-operation steps, determinant, adjugate for small matrices, identity verification, and numerical stability warnings.

Exact fractionsGauss–Jordan stepsA·A⁻¹ verificationUp to 6×6

Matrix A

Square matrices from 1×1 to 6×6.

Exact mode: fractions like 2/3 remain exact through the full row reduction. Typed decimals are converted to rational values exactly from their decimal text.

Inverse

Ready to calculate.

No inverse calculated yet.

det(A)

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Invertible?

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Verification

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Stability

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Row operations will appear here.
Calculate an inverse to verify A·A⁻¹ and A⁻¹·A.
For matrices up to 4×4, this tab shows adj(A) and confirms A⁻¹ = adj(A)/det(A).

Paste matrix

Export

Exact rational arithmetic is used for the inverse and determinant. The stability indicator is an infinity-norm condition-number estimate computed from decimal approximations; it is a practical warning, not a formal numerical-analysis certificate.