# Matrix calculator

> Calculate products, determinants, inverses and row reduction.

[Open tool](https://www.toolcabana.com/cu/matrix-calculator) · [Mathematics](https://www.toolcabana.com/cu/category/mathematics)

Tool ID: matrix-calculator. Requested language: cu. Description language: en. Complete guide translation: no; untranslated sections use English.

## Overview (en)

The Matrix calculator takes a matrix written as a JSON array of rows, such as [[1,2],[3,4]], and returns its determinant, inverse, transpose or reduced row echelon form, or its product with a second matrix. Matrices must be rectangular, numeric and no larger than 20 by 20. Results can be downloaded as matrix.json.

## Supported tasks (en)

Calculate products, determinants, inverses and row reduction.

## Steps (en)

1. Paste the source into the input editor, or load the built-in example.
2. Set operation, second matrix (json; for multiply).
3. Run matrix calculator, review the output, then use the available copy or download controls.

## Settings

- Operation (en; key: operation; type: select): determinant [en], inverse [en], transpose [en], rref [en], multiply [en]
- Second matrix (JSON; for multiply) (en; key: second; type: textarea)

## Limitations (en)

Local bounded calculations. Numeric inputs must be finite and within the visible ranges. Lists and tables have operation-specific limits. Models, estimates and supplied rates must be checked against your intended use.

## Example input

```text
[[1,2],[3,4]]
```

## Privacy and connections (en)

This operation processes its source in your browser. Copy and download are explicit actions; source input is not saved in an account or history.

## Questions (en)

### How do I enter a matrix?

Type it as a JSON array of rows, with each row in brackets: [[1,2],[3,4]] is a 2 by 2 matrix. Every row must have the same number of numeric entries, and the matrix can be at most 20 by 20.

### How do I multiply two matrices?

Enter the first matrix in the main input, choose multiply and put the second matrix in the second matrix field, also as JSON. The number of columns in the first must match the number of rows in the second.

### How does the calculator compute reduced row echelon form?

It uses Gauss-Jordan elimination with partial pivoting, picking the row with the largest absolute value in each column. Values smaller than 1e-10 are treated as zero pivots, and each pivot row is scaled so its leading entry is 1.

### Where is my input processed?

This operation processes its source in your browser. Copy and download are explicit actions; source input is not saved in an account or history.

### What are the input limits?

Local bounded calculations. Numeric inputs must be finite and within the visible ranges. Lists and tables have operation-specific limits. Models, estimates and supplied rates must be checked against your intended use.

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