Matrix Multiplication Calculator

Multiply matrices together. Free online matrix multiplication calculator with detailed steps.

The Matrix Multiplication Calculator computes the product of two matrices following the row-by-column multiplication rule. Matrix multiplication is central to linear algebra, transformations, computer graphics, and machine learning. Enter compatible matrices and see the full multiplication process with the resulting matrix.

Common use cases

  • Linear transformations
  • 3D graphics rotations
  • Neural network computations
  • Systems of equations
  • Markov chain calculations

How to use

  1. Enter dimensions for Matrix A (m × n)
  2. Enter dimensions for Matrix B (n × p)
  3. Input matrix values
  4. Click multiply to compute A × B
  5. View the step-by-step multiplication

FAQ

What are the dimension requirements?

Matrix A (m×n) can multiply B (n×p) if A's columns equal B's rows. Result is m×p.

Is matrix multiplication commutative?

No, usually AB ≠ BA. Order matters in matrix multiplication.

How is each element calculated?

(AB)ᵢⱼ = sum of (row i of A) × (column j of B), element by element, then summed.

What's the identity matrix?

The identity matrix I has 1s on diagonal, 0s elsewhere. AI = IA = A for any matrix A.