🔢 Determinant Calculator
Calculate the determinant of 2x2, 3x3, or 4x4 matrices. Step-by-step solutions using cofactor expansion.
Determinant Formulas
2 × 2 Matrix
|a b| = ad - bc
|c d|
3 × 3 Matrix (Sarrus Rule)
|a b c|
|d e f| = a(ei−fh) − b(di−fg) + c(dh−eg)
|g h i|
Properties
- det(A) = 0 → Matrix is singular (not invertible)
- det(A) ≠ 0 → Matrix is invertible
- det(A × B) = det(A) × det(B)
- det(AT) = det(A)