Find Matrix Inverse

Matrix inversion is where linear algebra stops being about copying numbers and starts being genuinely tricky. A single sign slip or rounding error corrupts the entire result, and by 4×4 the hand-written Gaussian elimination is a page of arithmetic that is nearly impossible to check. The inverse matrix — the operation that solves systems of equations, undoes transformations and powers regression — deserves a calculator that gets it exactly right.

Find Matrix Inverse computes A⁻¹ with exact rational arithmetic: the matrix is augmented with the identity and reduced using Gaussian elimination where every intermediate value is kept as an exact fraction of big integers. There is no floating-point rounding anywhere in the pipeline. The result is the true inverse as reduced fractions, optionally rendered as decimals, and singular matrices are detected and reported honestly. It is a precise answer to a problem that punishes imprecision.

• Exact fractions: BigInt rational arithmetic — every step exact, every result the true inverse.
• Fraction or decimal display: Flip between exact fractions and decimals with adjustable precision.
• Singular matrix detection: Zero pivots are caught and reported, never hidden.
• Up to 10×10 matrices: Large inverses stay exact instead of degrading into noise.
• Flexible input: Rows on lines, space or comma separated, or bracket notation — fractions like 1/2 are accepted too.
• Live computation: Edit any entry and the inverse recomputes instantly.
• Copy or download: Ready for notes, spreadsheets and code.
• Free and private: All computation happens in your browser; nothing is uploaded.

1. Enter a square matrix. Each row on its own line, entries separated by spaces or commas — or use bracket notation like [[2,1],[5,3]]. Fractions such as 1/2 are fine.
2. Check the size note. The tool confirms the dimensions it detected; matrices must be square.
3. Choose the display. Keep fractions for exact values, or switch to decimals and set the precision.
4. Read the inverse. The result appears instantly, aligned into columns.
5. Verify with the product. Multiply the matrix by its inverse mentally or with the tools — you should get the identity.
6. Copy or download. Take the result to your document or spreadsheet.

Example 1 — The classic 2×2. Paste "2 1 / 5 3". The exact inverse is [[3, −1], [−5, 2]], which the tool returns as fractions instantly — the textbook result, correct to the last digit.

Example 2 — Solving a system. The system 3x + 2y = 7, x − y = 4 can be solved via the inverse of [[3,2],[1,−1]]. Paste the matrix, read off the inverse, multiply by the constant vector — a complete solution without a single hand-arithmetic error.

Example 3 — Singular matrix. Paste "1 2 / 2 4". The rows are multiples of each other, so no inverse exists. The tool reports the matrix as singular rather than producing nonsense.

Example 4 — Fractions in the answer. A 3×3 like "1 1 1 / 0 1 1 / 0 0 1" gives an inverse full of −1s and 1s; paste "3 1 1 / 1 3 1 / 1 1 3" instead and read the fractional entries such as 1/4 — exactly, not 0.25-ish.

• Exact by construction: Rational arithmetic removes rounding error entirely.
• Trustworthy answers: Coursework, verification and applications get the true inverse.
• Honest failures: Singular matrices are named, not disguised.
• Two views of one result: Exact fractions and clean decimals in the same tool.
• Scales where floats fail: 10×10 inverses remain exact.
• Free and private: Runs entirely in the browser with nothing uploaded.