Matrices organise numbers in rows and columns and describe linear transformations, systems of equations, networks and images. This calculator is a quick all-in-one tool for the standard operations.
How to use the Matrix Calculator
- Choose the matrix size – the matching grid of fields appears.
- Enter the entries row by row (a₁ b₁ c₁ is the first row, a₂ b₂ c₂ the second, and so on).
- Read the result; integer matrices give exact fractions.
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Pick the operation; matrix B or the number k appear only when they are needed. Integer inputs give exact fraction results.
Formula
det, A⁻¹, Aᵀ, tr(A), rank, A ± B, A·B, k·A, Aⁿ
Worked example
Inputs — Size: 2 × 2; Operation: Determinant; A: a₁: 2; A: b₁: 1; A: a₂: 1; A: b₂: 4.
Results — Result = 7; Details = |A| = a₁·b₂ − b₁·a₂ = (2)(4) − (1)(1) = 7.
Key terms
- Matrix
- A rectangular array of numbers.
Frequently asked questions
How do I multiply two matrices?
Each entry is a row of A dotted with a column of B.
Can I add matrices of different sizes?
No – addition needs the same dimensions.
What is the trace?
The sum of the diagonal entries.
Why might the inverse not exist?
The determinant is zero.