🔲Matrix Calculator
Add, subtract, multiply matrices, or find the determinant and inverse — for 2×2 or 3×3 matrices.
Free Matrix Calculator
This matrix calculator handles the core operations for 2×2 and 3×3 matrices: addition, subtraction, multiplication, determinant, and inverse. Addition and subtraction combine matrices element by element; multiplication follows the row-by-column dot product rule; the determinant and inverse use cofactor expansion.
Matrices with a determinant of zero are singular and have no inverse — the calculator flags this rather than dividing by zero. Enter your values directly into the grid and every result updates instantly.
Useful for linear algebra coursework, systems of equations, and transformations. Free, runs entirely in your browser.
About the Matrix Calculator
Features
2×2 and 3×3 support
Switch sizes with one click.
Five operations
Add, subtract, multiply, determinant, and inverse.
Singular matrix handling
Clear error when a matrix has no inverse.
Instant, private
Runs entirely in your browser. No data is sent anywhere.
Frequently Asked Questions
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.