Matrix Algebra & Determinant Calculator
Perform fundamental linear algebra operations on 2x2 and 3x3 matrices. Calculate matrix multiplication (A × B), determinant |A|, matrix inverse A⁻¹, transpose Aᵀ, and scalar multiplication with step-by-step mathematical proofs.
How to Use Matrix Calculator (Determinant, Inverse & Multiplication)
Select Dimension
Choose 2×2 or 3×3 matrix dimensions.
Input Matrix Elements
Enter numerical values for Matrix A (and optional Matrix B for binary operations).
Choose Operation
Select Determinant, Inverse, Transpose, A + B, A - B, or A × B.
About Matrix Calculator (Determinant, Inverse & Multiplication)
A matrix is invertible if and only if its determinant is non-zero. The determinant represents the scaling factor of the transformation on an area (2D) or volume (3D). When det(A) = 0, the matrix collapses dimensionality and has no inverse.
Key Features
- Calculates Determinants with full cofactor expansion steps
- Finds Matrix Inverse using the Adjugate method: A⁻¹ = (1/det(A)) × adj(A)
- Matrix Multiplication with dot product row-by-column explanations
- Checks for singular (non-invertible) matrices where det(A) = 0
- Supports fractional and decimal matrix coefficients
Frequently Asked Questions
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