Matrix Calculator
Matrix A
Matrix B
Result
What is a Matrix Calculator?
A matrix calculator performs mathematical operations on matrices — rectangular arrays of numbers. This tool supports addition, subtraction, multiplication, determinant calculation, and transposition for 2×2 and 3×3 matrices. Matrices are fundamental in linear algebra, computer graphics, machine learning, and engineering.
How to Use
- Select the operation (Add, Subtract, Multiply, Determinant, or Transpose).
- Choose the matrix size (2×2 or 3×3).
- Fill in the values for Matrix A (and Matrix B if required). The result updates instantly.
Frequently Asked Questions
What is a matrix determinant?
The determinant is a scalar value computed from a square matrix that indicates whether the matrix is invertible (non-zero determinant = invertible). It's used in solving systems of linear equations, finding eigenvalues, and computing cross products in 3D geometry.
How is matrix multiplication different from regular multiplication?
Matrix multiplication is not element-wise. For A×B, entry (i,j) of the result = dot product of row i of A with column j of B. This makes matrix multiplication non-commutative (A×B ≠ B×A in general) and requires compatible dimensions.
What is a transpose matrix?
The transpose of matrix A (written Aᵀ) swaps rows and columns: entry (i,j) of Aᵀ = entry (j,i) of A. A 2×3 matrix transposed becomes 3×2. Symmetric matrices equal their own transpose.
What are matrices used for?
Matrices are fundamental in computer graphics (transformations, rotations), machine learning (neural network weights), engineering (structural analysis), economics (input-output models), and solving systems of linear equations.