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🧮 Matrix Calculator

Compute matrix addition, subtraction, multiplication, determinant, and inverse for up to 4×4 matrices. Ideal for linear algebra and system of equations checks.

Matrix Calculator

Work with 1×1 up to 4×4 matrices. Compute matrix addition, subtraction, multiplication, determinant, and inverse (when it exists) in a single, visual workspace.

Inputs

Supports up to 4×4

Matrix A size

Matrix B size

Matrix A

Matrix B

Matrix multiplication A×B is defined when columns of A match rows of B.

Results

A + B

A − B

A × B

det(A)

det(B)

Inverse of A

Only defined for square, non‑singular matrices. Try a 2×2, 3×3, or 4×4 with non‑zero determinant.

Inverse of B

Only defined for square, non‑singular matrices. Try a 2×2, 3×3, or 4×4 with non‑zero determinant.

Works great for linear algebra exercisesUse it to check hand‑worked Gaussian elimination

How to use this tool

Choose the dimensions for matrices A and B (from 1×1 up to 4×4).
Fill in the entries using real numbers (decimals allowed) for each matrix element.
Read off matrix addition, subtraction, multiplication, determinants, and inverses in the results panel.

Designed as a matrix inverse and determinant calculator

Quickly verify answers from linear algebra homework with a visual matrix calculator.
Experiment with different matrix sizes to see when matrix multiplication, determinants, and inverses are defined.
Use determinants and inverses to understand when systems of equations have unique solutions versus no or infinite solutions.

What this online matrix calculator supports

Matrix addition, subtraction, and multiplication for matrices up to 4×4.
Determinant computation via Gaussian elimination (determinant calculator for 2×2, 3×3, and 4×4).
Matrix inversion using an augmented matrix and row operations (matrix inverse calculator for square, non‑singular matrices).

FAQ

Can this matrix calculator handle very large matrices?: This tool focuses on small matrices (up to 4×4) ideal for teaching and exam questions rather than huge numerical problems or high‑dimensional numerical linear algebra.
How are determinants and inverses computed in this matrix inverse calculator?: Determinants use an elimination‑based approach and inverses are computed via Gauss–Jordan elimination on an augmented matrix [A | I], matching standard linear algebra techniques.
Why do I sometimes see no matrix inverse?: If a square matrix has determinant 0, it is singular and has no inverse. Try changing a row or column to make it full rank so the inverse exists.

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