Mathematics · Algebra
Matrix Calculator — Multiply, Determinant, Inverse, Transpose
Type matrices row by row (rows separated by semicolons) and add, subtract or multiply them, or find the determinant, inverse, transpose, rank, a power Aᵏ or a scalar multiple. The result is shown as a table, with a check that A × A⁻¹ gives the identity.
Your inputs
Quick start — try a typical case
Rows separated by ; — numbers by spaces or commas.
Your result Live
A × B
2 × 2 matrix
19 22 ; 43 50
- det(A)
- -2
A × B
2 rowsHow this is calculated
(AB)ᵢⱼ = Σₖ Aᵢₖ Bₖⱼ · A⁻¹ = adj(A) ÷ det(A) · det by row reduction
- A × B
- Needs A's column count to equal B's row count
Matrices add entry by entry. To multiply, each entry of the result is a row of A times a column of B, added up — so the order matters (A × B ≠ B × A in general). The determinant and inverse are found by row reduction; a matrix with determinant 0 squashes space flat and has no inverse.
Assumptions & sources
- Floating-point arithmetic; values within about 10⁻¹⁰ of zero are shown as 0.
Calculator ID MATH-MATRIX-001 · version 1.0.0
Common questions
How do I multiply two 2 × 2 matrices?
[1 2; 3 4] × [5 6; 7 8] = [19 22; 43 50]: e.g. the top-left entry is 1 × 5 + 2 × 7.
When does a matrix have no inverse?
When its determinant is 0 (it's 'singular') — for example [1 2; 2 4].
How do I enter a 3 × 3 matrix?
Separate rows with semicolons: 1 2 3; 4 5 6; 7 8 10.