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].