Matrix Multiplication Calculator

Matrix Multiplication Calculator

Multiply two matrices and see the product update as soon as the dimensions and entries are valid.

Last updated: June 2026 | By Patchworkr Team

Matrix Product Solver
Matrix A
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Matrix B
Result
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What Is Matrix Multiplication?

Matrix multiplication combines rows from the first matrix with columns from the second matrix. The inner dimensions must match for the product to exist.

How to Multiply Matrices

  1. Set the dimensions so the inner sizes match.
  2. Enter all matrix values.
  3. Multiply each row of A by each column of B.
  4. Sum the products to fill the result matrix.
C[i][j] = Σ A[i][k] × B[k][j]

Worked Example

[[1, 2], [3, 4]] × [[5, 6], [7, 8]] = [[19, 22], [43, 50]]

matrix product example

Frequently Asked Questions

What if the dimensions do not match?

The calculator rejects the input because the product is undefined when the inner dimensions differ.

Can I enter decimals?

Yes. Any finite real matrix entries are accepted, including decimal and scientific notation values.

Is the result always square?

No. The result dimensions are rows of A by columns of B.

What if a cell is blank?

Blank cells are rejected instead of being silently converted to zero.

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