Matrix Calculator
Add, subtract and multiply matrices; find determinants, inverses, transposes, powers and ranks, exactly with fractions.
Change the values and press Calculate to work out your own figures.
Two matrices: A + B, A − B, A × B
Enter A and B and choose an operation.
| Column 1 | Column 2 |
|---|---|
| 6 | 8 |
| 10 | 12 |
Show the working
- Entries are combined position by position.
One matrix: determinant, inverse, transpose, power, k × A, rank
Enter A and choose an operation (k for power or k × A).
Show the working
- Row-reduce A; the determinant is the product of the pivots (with a sign change for each row swap).
How to use it
Enter A and B and choose an operation. Enter A and choose an operation (k for power or k × A).
Number boxes accept whole numbers, decimals, fractions (3/4), powers (2^10), roots (sqrt(2)) and the constants pi and e. Show the working lists the steps.
Key facts
(AB)ᵢⱼ = Σₖ AᵢₖBₖⱼ; A⁻¹ by row reduction of [A | I]
Sizes
A + B needs equal sizes; AB needs A's columns to equal B's rows; determinants, inverses and powers need square matrices.
Questions
What is the determinant of [2, 4; 6, 8]?
2 × 8 − 4 × 6 = −8.
When is there no inverse?
When the determinant is 0.
Formulas
(AB)ᵢⱼ = Σₖ AᵢₖBₖⱼ; A⁻¹ by row reduction of [A | I]
Sources
Limitations
- Expressions up to 500 characters; matrices up to 10 × 10.
- Big-number results up to 100,000 digits; factorials up to 10,000!.
- Numbers in words up to 10^102 (short scale).