Matrix Calculator
Add, subtract, multiply matrices and find the determinant, transpose, and inverse of 2×2 and 3×3 matrices.
Matrix A
Matrix B
Result
What is Matrix Calculator?
A matrix calculator performs common matrix operations on 3×3 matrices: determinant, inverse, transpose, addition, and multiplication. Matrices are rectangular arrays of numbers used in linear algebra, computer graphics, physics simulations, machine learning, and engineering.
How to use
- 1 Select the operation using the tabs at the top: Det, Inv, Transpose, Add, or Multiply.
- 2 Fill in the values of Matrix A (and Matrix B if required for Add or Multiply).
- 3 Click the Calculate button to see the result.
- 4 For the determinant, a single scalar is shown; for other operations, the result matrix is displayed.
Formula
Example calculation
For the identity matrix, det = 1 and the inverse equals itself. For matrix addition, each element is added position by position. Multiplying a 3×3 by a 3×3 produces another 3×3 via dot products of rows and columns.
Frequently asked questions
What is a matrix determinant?
The determinant is a scalar value derived from a square matrix. It tells you if the matrix is invertible (det ≠ 0), and represents the scaling factor of the linear transformation the matrix represents.
When does a matrix have no inverse?
A matrix has no inverse (is singular) when its determinant is zero. This means the matrix collapses space to a lower dimension and cannot be reversed.
What is the transpose of a matrix?
The transpose flips a matrix along its diagonal — rows become columns and columns become rows. If A is m×n, then Aᵀ is n×m.
Is matrix multiplication commutative?
No. In general, A×B ≠ B×A for matrices. Matrix multiplication is associative and distributive but not commutative.
What size matrices does this calculator support?
This calculator works with 3×3 matrices for all operations. 3×3 covers a wide range of practical problems including 3D transformations and systems of three linear equations.