Matrix Calculator

Add, subtract, multiply or transpose real matrices up to six rows and columns, with clear dimension validation.

Result matrix[19, 22] [43, 50]

Separate columns with commas and rows with semicolons or newlines.

Result matrix

[19, 22] [43, 50]

  • Dimensions2 rows × 2 columns
Result matrix
Column 1Column 2
1922
4350

Real-valued matrices up to 6 × 6. Matrix multiplication is ordered: A × B generally differs from B × A.

How this was calculated

Each result entry is the dot product of a row of A and a column of B.

Formula and method

For A × B, each output entry is a row-column dot product. A’s column count must match B’s row count; addition requires identical dimensions.

Worked example

Multiplying [[1, 2], [3, 4]] by [[5, 6], [7, 8]] gives [[19, 22], [43, 50]].

Frequently asked questions

Does matrix multiplication depend on order?

Yes. A × B generally differs from B × A, and one order may be undefined even if the other is valid.

Last updated . Results are estimates for informational purposes only.