Matrix Multiplication Calculator (A × B)

Free Client-Side Step-by-Step

Multiply two matrices A×B with step-by-step visualization. Checks dimension compatibility (columns of A = rows of B). 100% client-side—no data sent to servers. Supports rectangular matrices up to 10×10.

Matrix A
×
One row per line, space separated
Matrix B
×
One row per line, space separated
Quick Examples
Result: A × B
Enter two matrices and click "Multiply A × B" to see the result.
Computation Steps
Detailed multiplication steps will appear here.

Exam-Style Practice

About This Matrix Multiplication Tool & Methodology

This matrix multiplication calculator computes C = A×B using the standard dot product formula. All computations run client-side in your browser—no matrices are sent to any server. Supports compatible dimensions (columns of A = rows of B) up to 10×10 with step-by-step solutions.

Authorship & Expertise

  • Author: Anish Nath
  • Background: Math and developer tools for education
  • Standards: Standard linear algebra (matrix product)

Trust & Privacy

  • Privacy: All calculations run locally; no data stored
  • Client-side: Your matrices never leave your device
  • Support: @anish2good

Matrix Multiplication: FAQ

When are two matrices compatible for A×B?

A×B is defined when columns(A) = rows(B). If A is m×n and B is n×p, the product C is m×p. Each cij is the dot product of row i of A with column j of B.

Is A×B the same as B×A?

No. Matrix multiplication is generally not commutative: A×B ≠ B×A. It is associative and distributive, and obeys (AB)^T = B^T A^T.

What sizes are supported?

This tool supports rectangular and square matrices with dimensions up to 10×10, showing step-by-step computations.

What dimension rules must I follow for matrix multiplication?

For A×B, the number of columns in A must equal the number of rows in B. If A is m×n and B is n×p, the result is m×p. Unlike addition, the matrices do not need the same dimensions.

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