Matrix Calculator
Perform matrix operations including addition, multiplication, determinant, and inverse calculations. Perfect for students, engineers, and professionals working with linear algebra.
Matrix Calculator
Perform matrix operations including addition, multiplication, determinant, and inverse calculations
Matrix Configuration
Matrix A
Matrix B
Matrix Operations
• Addition: A + B (same dimensions required)
• Multiplication: A × B (cols of A = rows of B)
• Determinant: det(A) (square matrices only)
• Inverse: A⁻¹ (square, non-singular matrices)
• Transpose: Aᵀ (rows become columns)
Understanding Matrix Operations
Matrices are rectangular arrays of numbers that are fundamental in linear algebra. They provide a compact way to represent and manipulate systems of linear equations, transformations, and data structures.
Our matrix calculator supports the most common matrix operations:
- Addition: Element-wise addition of matrices with the same dimensions
- Multiplication: Matrix multiplication following the rules of linear algebra
- Determinant: A scalar value that provides important information about a square matrix
- Inverse: The matrix that, when multiplied by the original, gives the identity matrix
- Transpose: Flipping a matrix over its diagonal
How to Use This Calculator
Matrix Operation Rules
Addition
Matrices must have the same dimensions. Add corresponding elements: (A + B)ᵢⱼ = Aᵢⱼ + Bᵢⱼ
Multiplication
For A × B, the number of columns in A must equal the number of rows in B. Result has dimensions rows(A) × cols(B).
Determinant
Only defined for square matrices. For 2×2: det(A) = ad - bc. For larger matrices, use cofactor expansion.