Matrix Calculator
Add, multiply, transpose and invert matrices, and find determinants, with the result laid out so you can check it against your own working.
Browser tool
Matrices
Enter numbers, decimals or fractions such as 1/3; up to 10×10. Arithmetic is exact, so 1/3 stays 1/3.
Paste A as text or CSV
Paste B as text or CSV
A × B
2×2
| 6 | −2 |
| 17 | −6 |
How this is calculated
About Matrix Calculator
Addition, multiplication, transposition, determinants and inverses, laid out so the result can be checked against your own working rather than merely trusted — which matters when the reason you are here is that the answer has to be shown as well as found. Free with no account needed. Every operation is evaluated by the browser instead of by a server somewhere.
How to use Matrix Calculator
- Set the dimensions and enter the valuesRows and columns first, then the entries. The tool rejects operations the dimensions do not permit.
- Choose the operationThe available ones depend on the shapes involved, which is itself informative.
- Read the resultLaid out as a matrix rather than a flat list, so it can be compared position by position.
Why multiplication is fussy about shapes
To multiply A by B, the number of columns in A must equal the number of rows in B, because each entry of the result is a dot product of one row with one column. That also makes multiplication non-commutative: AB and BA are different products, and frequently only one of them is even defined. It is the rule most often tripped over and the one that explains most "why will it not compute" moments.
What it does not do
- A singular matrix — determinant zero — has no inverse, and that is reported rather than approximated.
- Every entry is kept as an exact fraction rather than a rounded decimal, so long decimal inputs or high powers can produce fractions with very long numerators and denominators; the Decimals display rounds them to six places for reading.
- Large matrices are slow in a browser; this is sized for coursework rather than numerical computing.
Matrix Calculator: questions people ask
- Why can I not multiply these two matrices?
- Because the inner dimensions do not match: the columns of the first must equal the rows of the second. A 2x3 can multiply a 3x4; it cannot multiply a 2x3.
- What does a determinant of zero mean?
- The matrix is singular: it has no inverse, its rows are linearly dependent, and as a transformation it collapses space onto a lower dimension. Any system relying on inverting it has no unique solution.
- Can it find the reduced row echelon form (RREF) of a matrix?
- Yes. Choose "Row-reduced form and rank of A" and the matrix is reduced by Gauss–Jordan elimination with exact fractions, so 1/3 stays 1/3 rather than becoming a rounded decimal. Matrices up to 10×10 are supported, and the rank is reported alongside the result.
Questions about ToolsVerse itself — privacy, cost, what happens to your files — are answered in the frequently asked questions.
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