Matrix Multiplication Calculator
Calculate matrix multiplication instantly in your browser.
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What this tool does
Calculate matrix multiplication instantly in your browser. The worked default multiplies a 2×3 matrix by a 3×2 matrix to give a 2×2 product.
How to use the Matrix Multiplication Calculator
- Enter or select matrix a — rows separated by ; or new lines, entries by commas.
- Enter or select matrix b — same format as a.
- Read the calculated result; change any measurement to compare alternatives.
Formula
Each entry of A×B is the dot product of a row of A with a column of B: (AB)ᵢⱼ = Σ Aᵢₖ·Bₖⱼ. The product exists only when A's column count equals B's row count, and matrix multiplication is not commutative — A×B ≠ B×A in general.
- matrixA
- Matrix A — rows separated by ; or new lines, entries by commas
- matrixB
- Matrix B — same format as A
The worked default multiplies a 2×3 matrix by a 3×2 matrix to give a 2×2 product.
Worked example
For matrix multiplication calculator, the following measurements illustrate the exact method: Matrix A — rows separated by ; or new lines, entries by commas: 1, 2, 3; 4, 5, 6; Matrix B — same format as A: 7, 8; 9, 10; 11, 12.
Inputs
- Matrix A — rows separated by ; or new lines, entries by commas1, 2, 3; 4, 5, 6
- Matrix B — same format as A7, 8; 9, 10; 11, 12
Result
- Product A × B58, 64 ; 139, 154
- Product size2 × 2
- A size2 × 3
- B size3 × 2
Results explained
- Product A × B
- Product A × B from the formula above. The worked default multiplies a 2×3 matrix by a 3×2 matrix to give a 2×2 product.
- Product size
- Product size from the formula above. The worked default multiplies a 2×3 matrix by a 3×2 matrix to give a 2×2 product.
- A size
- A size from the formula above. The worked default multiplies a 2×3 matrix by a 3×2 matrix to give a 2×2 product.
- B size
- B size from the formula above. The worked default multiplies a 2×3 matrix by a 3×2 matrix to give a 2×2 product.
Frequently asked questions
Each entry of A×B is the dot product of a row of A with a column of B: (AB)ᵢⱼ = Σ Aᵢₖ·Bₖⱼ. The product exists only when A's column count equals B's row count, and matrix multiplication is not commutative — A×B ≠ B×A in general.
The worked default multiplies a 2×3 matrix by a 3×2 matrix to give a 2×2 product.
Where mathematically meaningful, yes. Fields specify permitted ranges and undefined operations display an error.
Exact integer calculations use safe integers; decimal calculations use browser floating point, so small rounding differences can occur.
All values remain in your browser and are never uploaded.