Matrix Calculator
Add, subtract, multiply, transpose, determinant, inverse, power and scalar operations on matrices up to 6×6 with step-by-step work.
Matrix A3×3
Trace0det0SymmetricYesSingularYes
Matrix B3×3
Operation
Two-Matrix
Matrix A
Matrix B
Result
0
0
0
0
0
0
0
0
0
3×3 matrix
Steps
- C is 3×3. Cᵢⱼ = Σ Aᵢₖ × Bₖⱼ
Matrix Operations Reference
Matrix Multiplication
For A×B, the number of columns in A must equal the number of rows in B. The result C has dimensions (rows of A) × (cols of B). Each entry Cᵢⱼ = Σ Aᵢₖ × Bₖⱼ.
Determinant
The determinant is a scalar value for square matrices. A determinant of zero means the matrix is singular (not invertible). Computed via Laplace expansion — efficient for matrices up to 6×6.
Matrix Inverse
The inverse A⁻¹ satisfies A × A⁻¹ = I (identity matrix). Only square, non-singular matrices have an inverse. Computed via Gauss-Jordan elimination on the augmented matrix [A|I].