Matrix Factorization and Determinant

https://kitchingroup.cheme.cmu.edu/blog/2013/04/01/Computing-determinants-from-matrix-decompositions/

1. A = PLU,

   det(L) = 1
   det(U) = Product of diagonal elements
   det(P) = (-1)^p

    p can be calculated by   dim - (sum of diagonal of P) - 1, 
    만약 diagonal이 1이면 안바뀐 것이고, 0이번 바뀐 것이므로