Matrix Calculator
Multiply, add and subtract matrices, and find the determinant, inverse, transpose and rank — or solve a system of linear equations Ax = b.
How to use
- 1Enter matrix A one row per line (numbers separated by spaces or commas).
- 2Choose the operation; for A×B or A+B also enter B, and for a system enter the right-hand side b.
How it's calculated
Determinant and inverse by Gauss-Jordan elimination with partial pivoting. A system Ax = b is solved as x = A⁻¹b when det(A) ≠ 0.
Frequently asked questions
When does a matrix have no inverse?
When its determinant is 0 (it's singular) — its rows are linearly dependent.
When can I multiply A by B?
When A has as many columns as B has rows. The result has A's rows and B's columns.
How do I solve 2x + 3y = 8, x − y = 1?
Enter A as '2 3' and '1 -1', choose 'Solve Ax = b' and enter b as '8, 1'. The answer is x = 2.2, y = 1.2.