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Matrix Calculator

Calculate the determinant, inverse, transpose, rank and square of a matrix, or add, subtract and multiply two matrices. Any size. Free matrix calculator.

Determinant
-9
Size
3 × 3
Invertible
Yes

Matrix operations in your browser

Type a matrix with one row per line and spaces between the numbers. The determinant tells you whether a square matrix can be inverted: the example 3 × 3 matrix has a determinant of −9, so it has an inverse. Multiplying A × B needs A's column count to equal B's row count, and each entry is a row of A times a column of B. Adding and subtracting work entry by entry on matrices of the same size. The calculator uses Gaussian elimination with partial pivoting for accuracy.

How to use it

  1. 1

    Enter matrix A

    One row per line, numbers separated by spaces.

  2. 2

    Choose an operation

    Or switch to two matrices for A × B, A + B or A − B.

  3. 3

    Read the result

    A number (determinant, rank) or a matrix.

Frequently asked questions

When does a matrix have an inverse?

When it's square and its determinant isn't zero.

Is matrix multiplication commutative?

No. A × B and B × A are usually different, and one may not even exist.

What is the rank?

The number of linearly independent rows: the dimension of the space the matrix spans.

Is anything stored?

No. The calculation runs in your browser.

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