I came across this strange property :

A = 1365636947370912401969102170896050049833536043036222945024106106365095957448673476595717951882200
B = 1353221295111631852153727244194823890765967481385223615864962219103729677003203245224034685374611

1. Why $0\not\in \{(B \times 11^n \bmod A) \bmod 11 \text{ : } n \in \mathbb N \} = \{ 1,2,3,\ldots,10\} \text{?}$
2. Is there a more general property behind it?