Matrix Operations Calculator
Add, subtract, multiply, or invert 2×2 and 3×3 matrices. Get determinant and basic properties.
Inputs
Determinant
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Trace (sum of diagonal)
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Rank
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Invertible?
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Sum of all entries
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About Matrix Operations Calculator
When determinant is zero
The matrix is singular — rows or columns are linearly dependent. Geometrically, it collapses space (3D → 2D plane, etc.). Singular matrices cannot be inverted.
Real-world matrix uses
Computer graphics (3D rotations/scaling), economics (Leontief input-output), physics (rotation/inertia), statistics (regression normal equations), neural networks.
For bigger matrices
Beyond 4×4, hand calculation becomes impractical. Use NumPy (Python: np.linalg.det), MATLAB, or Mathematica. LU/QR decomposition is the standard production algorithm.