Matrix multiplication: (AB)ᵢⱼ = Σₖ Aᵢₖ·Bₖⱼ. Requires cols(A) = rows(B). If A is m×n and B is n×p, then AB is m×p. Not commutative: AB ≠ BA in general. Associative: (AB)C = A(BC). Distributive: A(B+C) = AB+AC.
How to Use
Enter two matrices:
- Matrix A: Set dimensions, fill values
- Matrix B: Cols of A must match rows of B
- Result: Product matrix shown
Key Rules
- AB ≠ BA (not commutative)
- (AB)C = A(BC) (associative)
- AI = IA = A (identity)
- (AB)ᵀ = BᵀAᵀ
Applications
3D graphics transforms, neural network layers, Markov chains, control systems, image processing, quantum gates.
Step-by-Step Instructions
- 1Set Matrix A dimensions.
- 2Fill Matrix A values.
- 3Set Matrix B dimensions.
- 4Fill Matrix B values.
- 5View the product matrix.