determinant

1. $ det(A) $ ⇔  A is singular 

2. A가 rank deficient ⇔ $det(A) = 0$

3. diagonal matrix일 때, $det(A) = a_{11}a_{22}a_{nn}...$
4. triangular matrix일 때, $det(A) = a_{11}a_{22}a_{nn}...$

5. 항등행렬의 det = 1

6. $det(CA) = C^{n}det(A)$

7. $ det(A^{T}) = det(A) $

8. $det(AB) = det(A)dety(B)$

9  $det(A^{-1}) = \frac{1}{det(A)}$

10. $det(A) = \lambda_1\lambda_2\lambda_3...$