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Matrix Determinant Calculator - 2x2 and 3x3
Free matrix determinant calculator. Calculate determinants of 2x2 and 3x3 matrices. Check if matrix is invertible.
Matrix Determinant Calculator
Calculate matrix determinants
Determinant Result
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Matrix Determinant Calculator
Calculate the determinant of a square matrix. The determinant tells you if the matrix is invertible and its scaling factor.
Determinant Formula
2×2: det = a₁₁a₂₂ - a₁₂a₂₁
For 2×2: multiply diagonals, subtract. For 3×3: use cofactor expansion. det ≠ 0 means matrix is invertible.
Frequently Asked Questions
What does the determinant mean?
Geometrically: area/volume scaling factor. det = 0 means matrix collapses space (not invertible). Negative det means orientation flip.
When is determinant useful?
Solving linear systems (Cramer's rule), checking invertibility, calculating eigenvalues, computing cross products.
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