Can A still be a key if two tuples are the same
Pragmatically, You are correct that when you declare something as a primary key, that it must correspond to one tuple.  Databases will not allow you to store a tuple in a table if the primary key already exists for a tuple in the table.

Theoretically, If $R$ is a relation with the following set A of attributes $\{a_1, a_2,..., a_n\}$, then a primary key on the relation $R$ would be a subset $P \subset A$ such that for $F:P \rightarrow A$, we have $\forall x,y \in P $ $F(x)=F(y) \rightarrow x=y$.  This basically just means that the primary key forms a one-to-one mapping from the domain of keys to the range of corresponding tuples.  

If you have that two tuples are the same $A$ and $B$, then this implies that $A = B$,and we still have that $F(A)=F(B)$ so that there is no violation, in that sense.