Matrix Multiplication Calculator

Product A × B and interpretation

Vertical bars separate complete rows in the main product display. The table repeats those rows individually, and product dimensions state the resulting row and column counts.

To combine values with explicitly unequal weights, use the Weighted Average Calculator and follow its own input conventions.

The formula

Every output entry is a dot product between a row of A and a column of B. The number of columns in A must equal the number of rows in B; output shape uses A’s rows and B’s columns.

How to use this calculator

1. Enter Matrix A with one row per line and comma- or space-separated entries.
2. Enter Matrix B and check that its row count equals A’s column count.
3. Read the product dimensions and each output row in the result table.

Matrix Multiplication input conventions

Matrix multiplication combines a row of the first matrix with a column of the second. It is not element-by-element multiplication. A matrix with m rows and k columns can multiply a second matrix with k rows and n columns; the result has m rows and n columns. The inner dimension must match even when both input matrices are rectangular.

Interpreting product a × b

The order of multiplication matters. A × B can differ from B × A, and reversing the order can make the dimensions incompatible. Use one line for each row and avoid missing entries between separators. The result uses vertical bars to separate complete rows, with a table providing the same rows individually. This calculator handles real entries and does not evaluate matrix powers or find an inverse.

Assumptions & limitations

What this calculation assumes

• Rows of B correspond to columns of A in their given order.

What to keep in mind

• Two real matrices up to eight rows and columns each; finite-precision arithmetic.

Common questions