Matrix Operations
Master matrix mathematics with our interactive solvers. From basic operations to advanced concepts, each calculator provides step-by-step solutions with LaTeX output.
Basic Operations
Fundamental matrix arithmetic
Matrix Addition
Add two matrices component-wise
Scalar Multiplication
Multiply by a scalar
Multiplication
Matrix products and powers
Matrix Multiplication
Multiply two matrices with compatible dimensions
Matrix Power
Raise a square matrix to an integer power
Matrix Properties
Characteristics and invariants
Determinant
Calculate det(A) with step by step cofactor expansion
trace
Sum of diagonal elements
Transpose
flip a matrix over its diagonal
Advanced Operations
Cofactors, adjugates, and inverses
Matrix Inverse
Find A⁻¹ using adjugate method
Cofactor Matrix
Matrix of cofactors C_{ij} = (-1)^{i+j} det(M_{ij})
Adjugate Matrix
Transpose of cofactor matrix, adj(A) = C^T
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Why Our Matrix Calculator Stands Out
Built for students, by someone who understands the pain of learning linear algebra
Step-by-Step Work
Every calculation broken down with clear explanations
LaTeX Output
Copy beautifully formatted results to your homework
Exact Arithmetic
Fractions and symbols preserved - no decimal approximations
Smart Validation
Real-time dimension checking and compatibility alerts
Special Case Detection
Identifies singular, symmetric, and other special matrices
Mobile Optimized
Perfectly usable on phones and tablets
Shareable Links
Share your calculations with classmates
3D Visualization
Coming soon: see matrices transform space
Quick Matrix Size Guide
10×10 Maximum
Basic operations support up to 10×10 matrices
4×4 for Inverse
Inverse and determinant limited to 4×4 for performance
6×6 for Cofactors
Cofactor and adjugate support up to 6×6
Frequently Asked Questions
Why can't I compute the inverse of a 5×5 matrix?
Inverse calculation is computationally intensive. We limit it to 4×4 to maintain performance and provide detailed step-by-step explanations.
What does "singular matrix" mean?
A singular matrix has determinant = 0 and is not invertible. Our calculator will detect this and explain why.
Can I use fractions and decimals?
Yes! Enter "1/3" for fractions, "0.5" for decimals, or even symbols like "π". Our engine preserves exact values.
What's the difference between cofactor and adjugate?
The cofactor matrix contains signed minors. The adjugate is its transpose. They're related by adj(A) = C^T.
Ready to master matrix operations?
Choose an operation above and start calculating with step-by-step guidance. All calculators are free and always will be.