ToolHop.

ADVERT

Matrix Calculator

Compute matrix addition, subtraction, multiplication, determinant, inverse, transpose, rank, and RREF for up to 4×4 matrices with exportable results.

Inputs

Supports up to 4×4
×
×
Matrix A
Matrix B
Matrix multiplication A×B is defined when columns of A match rows of B.

Results

A + B
00
00
A − B
00
00
A × B
00
00
det(A)
0
det(B)
0
rank(A)
0
rank(B)
0
Aᵀ (transpose)
00
00
Bᵀ (transpose)
00
00
RREF(A)
00
00
RREF(B)
00
00
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

  1. Choose dimensions for matrices A and B (1x1 up to 4x4), then optionally apply quick zero or identity presets.
  2. Enter matrix entries and review arithmetic operations, determinant, inverse, transpose, rank, and RREF.
  3. Copy or download the full results report as JSON for QA logs or homework review.

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 4x4.
  • Determinant computation via Gaussian elimination (determinant calculator for 2x2, 3x3, and 4x4).
  • Matrix inversion using an augmented matrix and row operations (matrix inverse calculator for square, non-singular matrices).
  • Transpose, reduced row echelon form (RREF), and rank for quick linear algebra diagnostics.

FAQ

Can this matrix calculator handle very large matrices?
This tool focuses on small matrices (up to 4x4) 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.

ADVERT

More like this

ADVERT