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.