Matrix Calculator
Perform matrix operations including addition, subtraction, multiplication, determinant, transpose, and inverse with detailed step-by-step solutions.
Matrix Operation
Matrix A
Rows:
Cols:
Matrix B
Rows:
Cols:
Result
Configure matrices and select operation
Matrix Operations Guide
Addition & Subtraction
• Matrices must have same dimensions
• Add/subtract corresponding elements
• (A + B)ᵢⱼ = Aᵢⱼ + Bᵢⱼ
Multiplication
• Columns of A = Rows of B
• Result size: (A rows) × (B cols)
• (AB)ᵢⱼ = Σ Aᵢₖ × Bₖⱼ
Transpose
• Swap rows and columns
• (Aᵀ)ᵢⱼ = Aⱼᵢ
• Size changes from m×n to n×m
Determinant
• Only for square matrices
• 2×2: ad - bc
• 3×3: Use cofactor expansion
• Zero determinant = singular matrix
Inverse
• Only for square, non-singular matrices
• A × A⁻¹ = I (identity matrix)
• 2×2: A⁻¹ = (1/det(A)) × adj(A)
Frequently Asked Questions
Common matrix operations include addition, subtraction, multiplication, finding the determinant, transpose, and inverse. Each operation has specific requirements for matrix dimensions.
Tips
- Enter the dimensions in the same unit for consistency.
- Results update automatically as you type.
- Use the unit selector to convert between different measurement systems.