Matrix Calculator
Determinant, inverse, RREF, powers and products of matrices, as exact fractions.
Linear Algebra In Exact Fractions
Enter one or two matrices — whole numbers, decimals or fractions like 2/3 — and compute the determinant, inverse, transpose, reduced row echelon form, a power, a product, a sum or a difference, or solve AX = B for a system of linear equations.
Every step is done in exact rational arithmetic. Floating-point elimination piles up rounding error until a determinant that should be zero comes out as 1e-16 and a singular matrix appears to have an inverse; here a zero is a zero and an inverse is written as the fractions it really contains.
Key features
- Determinant, inverse, RREF and rank of any square or rectangular matrix.
- Multiply, add, subtract and raise to a power.
- Solve linear systems AX = B, several right-hand sides at once.
- Exact fractions — no rounding error, ever.
- Up to 8 × 8, with a grid you can resize and tab through.
This tool runs entirely inside your browser using native Web APIs. Your files and text are never uploaded to a server, never logged and never shared with third parties.
How to use: Matrix Calculator
- Set the size
Choose rows and columns for A, and B if the operation needs it. - Fill in the entries
Tab moves between cells; fractions such as −3/4 are fine. - Pick the operation
Determinant, inverse, RREF, transpose, power, product or solve. - Copy the result
Results are shown as exact fractions and can be copied as text.
Technical specifications
| Processing location | Entirely in your browser — no server round trip |
|---|---|
| Data uploaded | None. Files and text never leave your device |
| Price | Free — no account, no trial, no usage cap |
| Category | Calculators |
| Works offline | Yes, once the page has loaded |
| Browser support | Chrome 90+, Edge 90+, Firefox 90+, Safari 15+ |
| Interface languages | English, 中文, हिन्दी, Español, العربية |
Frequently asked questions
How do I find the inverse of a matrix?
Choose Inverse. The calculator row-reduces [A | I]; if A reduces to the identity, the right half is A⁻¹. If the determinant is zero the matrix is singular and has no inverse, and the tool says so rather than printing enormous numbers.
What is reduced row echelon form used for?
RREF shows the rank of a matrix, which columns are pivots, and the solutions of the system the matrix represents. A row of zeros ending in a non-zero value means the system has no solution; a free column means infinitely many.
How do I solve a system of linear equations?
Put the coefficients in A and the constants in B as a single column, then choose Solve. For 2x + y = 5 and x − y = 1, A is [[2, 1], [1, −1]] and B is [[5], [1]], giving x = 2 and y = 1.
Why does matrix multiplication fail?
A × B needs as many columns in A as rows in B. A 2 × 3 matrix can multiply a 3 × 4 matrix, giving 2 × 4, but not the other way round — multiplication is not commutative.
Why use fractions instead of decimals?
Because decimals like 1/3 cannot be stored exactly, and elimination multiplies the error. Exact arithmetic gives textbook answers you can check by hand.