# Matrix Calculator - Add, Multiply, Determinant, Inverse and Rank

> Free online matrix calculator: add, subtract and multiply matrices up to 8×8, transpose, and compute the determinant, inverse, matrix power and rank.

- URL: https://qilingtools.com/en/math/matrix
- Category: Math Tools (https://qilingtools.com/en/math)
- Tags: [Math](https://qilingtools.com/en/tags/math), [Education](https://qilingtools.com/en/tags/education), [Algorithms](https://qilingtools.com/en/tags/algorithm)
- Last updated: 2026-10-26
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Type the entries into the grid and get matrix addition, subtraction, multiplication, transpose, determinant, inverse, rank and powers. Matrices up to 8×8 are supported and results are tab separated, ready to paste into Excel.

## How to use

1. Pick the operation and set the number of rows and columns
2. Fill in the entries — “Identity” and “Random” give you a quick start
3. The result appears below and can be copied in one click

## Features

- Add, subtract, multiply, transpose, determinant, inverse, rank, power
- Up to 8×8 with resizable dimensions
- Gaussian elimination with partial pivoting for stability
- Determinant view also reports the trace
- Tab-separated output for spreadsheets

## FAQ

### Why does it say the matrix is not invertible?

A square matrix with determinant 0 has no inverse. Check with the determinant view, or look at the rank to see whether it is full rank.

### What sizes does matrix multiplication need?

The columns of A must equal the rows of B; the result has the rows of A and the columns of B. Addition and subtraction need identical sizes.

### Why are there decimals in the result?

Inversion and division produce fractions. Values are shown to 6 significant digits and values very close to zero are displayed as 0.

### What is the largest matrix supported?

8×8. Larger problems belong in dedicated software — this tool targets classwork and quick checks.

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