Math

Matrix Multiplication Calculator

Multiply two matrices with step-by-step solutions. Learn matrix multiplication rules.

100% FreeStep-by-Step Solutions

Enter two matrices. Matrix A columns must equal Matrix B rows.

Matrix A: Rows

Matrix A: Columns

Matrix A

Matrix B: Rows (must = A columns)

Auto-set to match A columns

Matrix B: Columns

Matrix B

Try These Examples

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Example 1

2×2 matrices

Matrix Multiplication Rules

For matrices A (m×n) and B (n×p), the product AB is defined only when:

(AB)_{ij} = \\sum_{k=1}^{n} A_{ik} B_{kj}

Important Properties

Not commutative: AB ≠ BA (in general)

Associative: (AB)C = A(BC)

Distributive: A(B+C) = AB + AC