Matrix Multiplication Calculator

Use our free matrix multiplication calculator to multiply two matrices. The number of columns in A must equal the number of rows in B.

Math

Matrix A

Matrix B

Formula

Matrix multiplication computes (AB)ᵢⱼ = Σₖ Aᵢₖ Bₖⱼ. The number of columns of A must equal the number of rows of B. The result has dimensions rows(A) × columns(B). Matrix multiplication is NOT commutative.

(A × B)ᵢⱼ = Σₖ Aᵢₖ × Bₖⱼ

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Enter Matrix A (r×c dimensions).
2Enter Matrix B (c×p dimensions — c must match).
3Click Calculate to multiply.

Examples

2×3 × 3×2

1.Result is 2×2
2.AB₁₁ = 1×7+2×9+3×11 = 58
3.AB₁₂ = 1×8+2×10+3×12 = 64

Result: 58

3×1 × 1×3 (outer)

1.Result is 3×3 outer product

Result: 4

Frequently Asked Questions

When columns of A = rows of B.

No, A×B ≠ B×A in general (often not even defined).

Yes, (A×B)×C = A×(B×C).

I (identity matrix) where I×A = A×I = A.

Each element is the dot product of a row of A with a column of B.

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CalculateMe Team

Last updated: 2026-07-14

Matrix Multiplication Calculator

Formula

How It Works

Examples

2×3 × 3×2

3×1 × 1×3 (outer)

Frequently Asked Questions

When can I multiply?

Is it commutative?

Is it associative?

What is the identity?

Dot product?

Related Calculators

Matrix Multiplication Calculator

Formula

How It Works

Examples

2×3 × 3×2

3×1 × 1×3 (outer)

Frequently Asked Questions

When can I multiply?

Is it commutative?

Is it associative?

What is the identity?

Dot product?

Related Calculators