Matrix calculator
Calculate the determinant, inverse, transpose, sum, difference and product of matrices up to 6×6, with fractions when the result isn't a whole number.
Determinant, inverse and matrix operations
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Matrix calculator: what it is for
Choose the matrix size and the operation, fill in the values and see the result right away. The determinant and the inverse are calculated with Gaussian elimination, and results show as fractions when they aren't whole numbers. The tool tells you when the matrix has no inverse.
How to use
- Choose the size and the operation.
- Fill in matrix A (and B, if needed).
- Read the result.
When to use it
- Solve linear algebra exercises.
- Check 3×3 and 4×4 determinants.
- Calculate inverses for linear systems.
Frequently asked questions
How is the determinant calculated?
For 2×2 matrices, it is the product of the main diagonal minus the product of the other diagonal. For larger matrices, the calculator uses Gaussian elimination, which works for any size and gives the same result as the rule of Sarrus for 3×3.
When does a matrix have no inverse?
When the determinant is zero. The matrix is then called singular and the calculator tells you.
When can I multiply A by B?
When the number of columns of A equals the number of rows of B. In this calculator both matrices are the same size, so multiplication is always possible.
Is it really free?
Yes, 100% free. No sign-up, no subscription and no usage limits. All Tools123 tools are free and run right in your browser.