Matrix calculator
Add, subtract and multiply matrices, or find a determinant, inverse, transpose or power.
About this calculator
This matrix calculator does the main matrix operations: addition, subtraction, multiplication, determinant, inverse, transpose and powers.
Type each matrix one row per line, with the numbers separated by spaces. It works with matrices up to 10 rows by 10 columns.
How it works
Matrices are added entry by entry. In A × B, each entry is a row of A multiplied term by term with a column of B and summed. The determinant and inverse use Gauss-Jordan elimination, swapping rows to keep the arithmetic stable.
Last reviewed:
Worked example
- Operation: A × B
- Matrix A, one row per line: 2 1; 1 3
- Matrix B, one row per line: 1 2; 0 1
Result: [2, 5 ; 1, 5]
Common questions
How do you multiply two matrices?
Multiply each row of A by each column of B, entry by entry, and add the products. A must have as many columns as B has rows.
When does a matrix have no inverse?
When its determinant is 0. Such a matrix is called singular: one of its rows or columns can be made from the others.
Is A × B the same as B × A?
Usually not. Matrix multiplication isn't commutative, so the order matters.
Sources and further reading
The story behind it
Where the idea came from: James Joseph Sylvester coined the word matrix in 1850, and Arthur Cayley set out matrix algebra, including multiplication and inverses, in 1858.
Today matrices run computer graphics, search engines and machine learning, where enormous matrices are multiplied billions of times a second.
Why you can trust this calculator
- It runs in your browser. Nothing you type into it is sent anywhere.
- The method is explained on this page, so you can check it yourself.
- Free to use, with no sign-up.
- Results are estimates, so please double-check anything important.
- Spotted a mistake? Tell us and we'll look into it.
After 15 years as a mathematics educator, I built CalculStore to give students, teachers, professionals and anyone working with numbers simple, reliable tools.
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