Last updated: August 1, 2026
Matrix Multiplication Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
Enter Matrix A and Matrix B in row format, and the calculator will multiply them using standard row-by-column dot products when the inner dimensions match. The result includes the product matrix, its dimensions, and the total number of entries in that product.
Enter Matrix A and Matrix B in row form, and if the inner dimensions match the calculator returns the standard matrix product AB.
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
Each entry of AB is the dot product of a row of A with a column of B.
Where:
- A=left matrix
- B=right matrix
- AB=matrix product
Worked Examples
Multiply two 2×2 matrices
Compute [[1,2],[3,4]] · [[5,6],[7,8]].
- 1Pair rows of A with columns of B.
- 2Compute each dot product.
- 3Assemble the product matrix.
2×3 by 3×2 product
Multiply a rectangular pair with matching inner dimension.
- 1Check the inner dimensions.
- 2Compute each row-column dot product.
Identity multiplier
Multiplying by I leaves A unchanged.
- 1Use the identity columns.
- 2Read the original entries back.
Dimension mismatch
A 2×2 matrix cannot multiply a 3×2 matrix on the right.
- 1Compare columns of A with rows of B.
- 2Stop when the inner dimensions differ.
Introduction
Multiply Matrix A by Matrix B using standard row-by-column multiplication.
Overview
Multiply Matrix A by Matrix B using standard row-by-column multiplication.
Product matrix
Composing linear transformations
Applying matrices to vectors
Building matrix powers
Input format
Enter Matrix A and Matrix B in row form.
Separate rows with semicolons
Separate entries with commas or spaces
Brackets are optional
Keep row lengths consistent
Formula and method
Each entry of AB is the dot product of a row of A with a column of B.
- A matters:
left matrix.
- B matters:
right matrix.
- Ab matters:
matrix product.
Validation rules
The calculator uses deterministic validation before it computes the final result.
Both matrices must be rectangular
Columns of A must equal rows of B
Every entry must be finite
The result shape is rows of A by columns of B
Interpreting the outputs
Use the main result first, then the secondary fields to verify the structure and meaning of the answer.
productMatrix is the standard matrix product AB
dimensions confirms the size of the result
entryCount counts all numbers in the result
Order matters, so AB and BA are usually different
Common use cases
These are typical reasons to use this calculator in study or applied work.
Composing linear transformations
Applying matrices to vectors
Building matrix powers
Homework verification
FAQs
Why does order matter in matrix multiplication?
Because rows of the left matrix pair with columns of the right matrix.
How do I know if multiplication is allowed?
The number of columns in Matrix A must equal the number of rows in Matrix B.
What shape does the result have?
It has as many rows as Matrix A and as many columns as Matrix B.
Can I multiply rectangular matrices?
Yes, as long as the inner dimensions match.
Is this the Hadamard product?
No. This is standard row-by-column multiplication.
Can I use decimals?
Yes. Any finite real entries are supported.