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Matrix Calculator (Steps, Exact Fractions)

Add, subtract, multiply, transpose, and get the determinant, inverse or rank — with every row operation shown and entries kept as exact fractions.

Tool inputs stay in your browser · optional AI search sends your query

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Good to know: Pick the sizes, type whole numbers, fractions (1/3) or decimals, then press Calculate. Determinant, inverse and rank walk through Gaussian elimination row by row (R2 ← R2 − 2·R1) and every answer is kept as an exact fraction, so 1/3 stays 1/3 instead of drifting like a calculator that rounds. Inverses are checked by multiplying A × A⁻¹ and showing the identity. Matrices up to 5 × 5, arithmetic only — no symbolic algebra.

How to use it (step by step)

  1. 1Pick the size of A (and B, for the two-matrix operations), then type the entries: 3, -2/5 or 1.25 are all fine. Paste a block from a spreadsheet straight into a grid.
  2. 2Choose the operation — add, subtract, multiply, transpose, determinant, inverse or rank.
  3. 3Press Calculate. The answer is kept as an exact fraction, with the decimal underneath.
  4. 4Open “How it was calculated” to see every row operation (R2 ← R2 − 2·R1). For inverses, the tool also multiplies A × A⁻¹ and shows the identity so you can check it yourself.

Words to know

Fraction / ratio
A fraction is a part of a whole (3/4 = three of four parts). A ratio compares two amounts (2:1 = twice as much).
Matrix
A grid of numbers in rows and columns, used in math, graphics and engineering.

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