Matrix Calculator
Perform matrix operations and solve systems of linear equations
Matrix Operations
Addition & Subtraction
Matrices must have same dimensions
Add/subtract corresponding elements
Multiplication
Cols of A must equal rows of B
Result is (rows of A) × (cols of B)
Determinant
Only for square matrices
2×2: ad - bc
3×3: Use cofactor expansion
Inverse
Only for square matrices
A⁻¹ = adj(A)/|A|
AA⁻¹ = I
Benefits & Features
Our matrix calculator offers multiple advantages:
Comprehensive Operations
- Basic operations (add, subtract, multiply)
- Advanced operations (determinant, inverse)
- System of equations solver
- Eigenvalue calculator
- Step-by-step solutions
User-Friendly Interface
- Dynamic matrix size adjustment
- Clear result visualization
- Automatic dimension validation
- Mobile-responsive design
- Real-time calculations
Educational Features
- Detailed step-by-step solutions
- Matrix operation explanations
- Common matrix properties
- Practice problems
- Visual representations
Frequently Asked Questions
Matrix multiplication (A × B) is only possible when the number of columns in matrix A equals the number of rows in matrix B. Each element in the result is the sum of products of corresponding row elements from A and column elements from B. The result matrix has dimensions (rows of A) × (cols of B).
For a 2×2 matrix [[a,b],[c,d]], the determinant is ad-bc. For larger matrices, use cofactor expansion along any row or column. The determinant exists only for square matrices and is useful for finding inverses and solving systems of equations.
The inverse of a matrix A (written as A⁻¹) is a matrix that, when multiplied by A, gives the identity matrix. Not all matrices have inverses - only square matrices with non-zero determinants are invertible. The inverse is useful in solving systems of equations and other applications.
To solve a system Ax = b: 1) Write the coefficients as matrix A and constants as vector b, 2) If A is invertible, multiply both sides by A⁻¹, 3) The solution is x = A⁻¹b. Alternatively, use Gaussian elimination to solve the augmented matrix [A|b].