Understand the subject
What is matrix multiplication?
Matrix multiplication composes relationships: each output entry combines one row of A with one column of B.
Use it for chained linear transformations, systems, and compatible table relationships.
See the structure
What the calculation is doing
1234
row 1 · column 12012
1×2 + 2×1 = 4Worked interpretation
Read the result in context
(AB)ᵢⱼ = Σₖ aᵢₖbₖⱼ
Interpret with care
Important boundary
A’s columns must equal B’s rows, and reversing order can change the result or make it undefined.
Use the Matrix Calculator to experiment with small exact matrix operations before applying a more specialized route.
Quick guide
How to use this calculator
- Set A's columns equal to B's rows.
- Enter every value in A and B.
- Read the exact product AB; reversing the matrices can give a different result.
Calculation method
Take row-column dot products
The entry in row i and column j of AB is the sum of products between row i of A and column j of B.
Worked example
Multiply a row by a column
For A = [[1,2],[3,4]] and B = [[2,0],[1,2]], calculate four row-column dot products.
AB = [[4,4],[10,8]]
Supported inputs
Precision and limits
Matrix size
Each input matrix may contain 1–6 rows and 1–6 columns.
Entry precision
Each signed decimal may contain up to 30 digits and 15 decimal places.
Exactness
Finite decimals are converted to reduced fractions before calculation; matrix arithmetic is not rounded.
