Matrix Inputs
Matrix A
Matrix B
Used for scalar multiplication (k × A)
Operations
Result
Select an operation and click Calculate.
How to Use the Matrix Calculator
- Set sizes — Choose grid size (2×2 to 5×5) independently for Matrix A and Matrix B.
- Enter values — Click each cell and type a number. Use Random Fill to populate with test values.
- Select operation — Click the operation button (A+B, A−B, A×B, det(A), A⁻¹, Aᵀ, or k×A).
- Calculate — Press the Calculate button to see the result and step-by-step breakdown.
Supported Operations
| Operation | Description | Requires |
|---|---|---|
| A + B | Element-wise addition | Same dimensions |
| A − B | Element-wise subtraction | Same dimensions |
| A × B | Matrix multiplication | A cols = B rows |
| det(A) | Determinant with cofactor steps | Square matrix A |
| A⁻¹ | Inverse via Gauss-Jordan | Square, non-singular A |
| Aᵀ | Transpose of A | Any matrix A |
| k × A | Scalar multiplication | Any matrix A |
What is a Matrix?
A matrix is a rectangular array of numbers arranged in rows and columns. Matrices are fundamental to linear algebra, computer graphics, machine learning, physics simulations, and engineering.
- Square matrix: same number of rows and columns (required for determinant/inverse)
- Determinant: a scalar value encoding geometric scaling; zero means the matrix is singular
- Inverse: A⁻¹ such that A × A⁻¹ = I (identity matrix)
- Transpose: rows become columns and vice versa