Question: Cholesky Decomposition

Ok If R is the Cholesky decomposition of the Covariance matrix then I need:

i) Cov=R*R'
ii) R'=R

I can show that i) indeed holds but ii) does not seem to work. Why?

restart:
with(LinearAlgebra):
Cov := Matrix([[.1, .2], [.2, 1.3]]);
Ap := LUDecomposition(Cov, 'method' = 'Cholesky');

Cov = Ap.Transpose(Ap);
Ap = Transpose(Ap)

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