Matrix Calculator

Add, subtract, and multiply 2×2 or 3×3 matrices, or transpose, find the determinant, and invert a single matrix. Calculates in your browser.

Matrix A

Matrix B

Result

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Show the math

Matrices add element-wise, multiply row-by-column, and invert via Gauss–Jordan elimination:

(AB)ᵢⱼ = Σₖ Aᵢₖ Bₖⱼ  ·  A⁻¹A = I

A matrix only has an inverse when its determinant is non-zero. All math runs in your browser.

What this does

A matrix calculator adds, subtracts, and multiplies 2×2 or 3×3 matrices, or transposes, finds the determinant, and inverts a single matrix.

How to use it

  1. Choose the matrix size.
  2. Enter the matrix values.
  3. Pick the operation.
  4. Read the resulting matrix or value.

How it works

Two-matrix operations need compatible sizes; single-matrix operations give transpose, determinant, and inverse. A matrix is invertible only when its determinant is non-zero.

Understanding your result

The determinant is the value to check first, because a matrix is invertible only when it is non-zero; a zero determinant means the matrix is singular and has no inverse, which usually signals a system with no unique solution. Remember multiplication is not commutative (A times B differs from B times A) and needs compatible dimensions, unlike addition.

Example

A 2×2 with determinant 0 is singular and has no inverse.

Sources & methodology

Last updated .

Frequently asked questions

What operations are supported?

Addition, subtraction, and multiplication of two matrices, plus transpose, determinant, and inverse of a single matrix, for 2×2 and 3×3 sizes.

Why can a matrix have no inverse?

A matrix is invertible only when its determinant is non-zero; a zero determinant means it is singular and cannot be inverted.

Is my data stored?

No. Everything is calculated locally in your browser.