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Matrix Calculator

Add, multiply, transpose, invert and find determinants.

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Matrix A

Matrix B

Result

Determinant of A

—

Properties of A

Dimensions—
Trace—
Rank—
Invertible—

—

What kind of matrix A is

Matrix multiplication is not commutative, so A × B and B × A are offered separately and are generally different. Only a square matrix with a non-zero determinant has an inverse; a zero determinant means the rows are linearly dependent. Inversion uses Gauss-Jordan elimination with partial pivoting.

Quick Tool Overview

The Matrix Calculator performs the standard operations on matrices up to 5×5 — addition, subtraction, multiplication, scaling, transposition and inversion — with the determinant, trace and rank reported for square matrices.

What it does
Adds, multiplies, transposes and inverts matrices
You give it
One or two matrices of up to five rows and columns
You get back
The result matrix plus determinant, trace and rank
Best for
Linear algebra coursework and checking hand calculations
Calculators Free, unlimited use No sign-up Runs in your browser

About the Matrix Calculator

Perform the standard matrix operations on matrices up to five by five: addition, subtraction, multiplication, scalar multiplication, transposition and inversion, with the determinant, trace and rank reported for square matrices.

Two things about matrix arithmetic catch people out, and the calculator surfaces both. Multiplication is not commutative — AB and BA are generally different matrices, and may not even both be defined — so the order you enter them in matters. And a matrix is invertible only when its determinant is non-zero; a zero determinant means the rows are linearly dependent and no inverse exists, which is reported explicitly rather than as a wall of infinities. Inversion uses Gauss-Jordan elimination with partial pivoting for numerical stability.

Key features of the Matrix Calculator

Every standard operation

Add, subtract, multiply, scale, transpose and invert, with dimension checks that explain any mismatch.

Gauss-Jordan inversion

Inversion uses partial pivoting for numerical stability rather than a naive cofactor expansion.

Singular matrices explained

A zero determinant means no inverse exists, and the tool says that rather than returning infinities.

Order matters, and it says so

Matrix multiplication is not commutative, so AB and BA are offered separately.

Determinant, trace and rank

The three properties most often asked for alongside an operation, computed automatically.

How to use the Matrix Calculator

  1. 1

    Set the dimensions

    Choose the size of each matrix, up to five rows and columns.

  2. 2

    Fill in the values

    Type into the grid. Decimals and negatives are fine.

  3. 3

    Pick an operation

    Add, subtract, multiply, scale, transpose or invert.

  4. 4

    Read the result

    The resulting matrix, plus determinant, trace and rank where they apply.

Frequently asked questions

Each entry of the product is the dot product of a row of the first matrix with a column of the second. The number of columns in the first must equal the number of rows in the second.

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