Frequently Asked Questions
Everything you need to know about the Matrix Calculator.
How do you add or subtract matrices?
Add or subtract the corresponding elements in each position — both matrices must be the same size for this to work.
How does matrix multiplication work?
Each element of the result is the dot product of a row from matrix A and a column from matrix B — multiply corresponding entries and sum them.
What is the determinant?
The determinant is a single number computed from a square matrix that indicates properties like whether it's invertible, and it relates to how the matrix scales area or volume.
What does it mean if the determinant is zero?
A determinant of zero means the matrix is 'singular' — it has no inverse, and its rows or columns are linearly dependent.
How is the inverse of a matrix calculated?
For 2×2 matrices, swap the diagonal elements, negate the off-diagonal elements, and divide by the determinant. For 3×3, the calculator uses the cofactor/adjugate method: compute the matrix of cofactors, transpose it, and divide by the determinant.
Is matrix multiplication commutative?
No — in general, A × B does not equal B × A for matrices, unlike ordinary number multiplication.
Does this support matrices larger than 3×3?
No, this calculator supports 2×2 and 3×3 matrices only, the sizes most commonly used in introductory linear algebra.
Why does the second matrix input disappear for determinant and inverse?
Determinant and inverse are single-matrix operations that only use matrix A, so matrix B isn't needed for those calculations.
What's a common use for the matrix inverse?
The inverse is used to solve systems of linear equations written in matrix form (Ax = b becomes x = A⁻¹b), among other applications in transformations and computer graphics.
Is this calculator free to use?
Yes, completely free with no sign-up, and it runs entirely in your browser.