Multiplying
[1 2; 3 4] × [5 6; 7 8] = [19 22; 43 50]. The determinant of [1 2; 3 4] is −2.
Matrix Calculator
Add, subtract and multiply matrices, and find the determinant, inverse and transpose.
One row per line, numbers separated by spaces
Result
Result (2 × 2)
| 19 | 22 |
| 43 | 50 |
Runs in your browser — nothing you enter is sent to a server.
How the Matrix Calculator works
Type each matrix with one row per line and the numbers separated by spaces or commas (or rows separated by semicolons). Choose an operation and the result updates as you type.
- A + B and A − B work element by element and need matrices of the same size.
- A × B needs A's columns to match B's rows; each entry is a row of A times a column of B.
- Determinant and inverse need a square matrix; they use Gaussian elimination with partial pivoting.
Formulas
Matrix product
(AB)ij = Σk Aik × Bkj
2 × 2 determinant and inverse
det = ad − bc; inverse = (1 ÷ det) × [d −b; −c a]
Examples
An inverse
The inverse of [4 7; 2 6] is [0.6 −0.7; −0.2 0.4] (its determinant is 10). [1 2; 2 4] has no inverse: its determinant is 0.
Frequently asked questions
Why is A × B different from B × A?
Matrix multiplication isn't commutative: the order changes the result, and often the size.
Why does my inverse show tiny numbers like 0.0000000001?
Results are rounded to 10 decimal places; values that are 0 apart from rounding error are shown as 0.
How large can the matrices be?
Up to 10 × 10.
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