I'm not thinking about this from my perspective, however. I'm in a way thinking of it from an outsider's perspective.

In terms of "me", there would be two individual instances of me that open their eyes and either see A or B. The "original" is determined by you the question-asker, and the fact that that "original" walked into chamber A. Because that "original" walked into chamber A, that "original" would see the letter A, whereas the clone would see the letter B. Its possible that the "original" was, at time of cloning, completely recreated/rearranged. However, that "original" would retain the A designation/"originality" because to an observer, someone walked into a chamber with no other exits, and exited out the same chamber, that someone is the same person.

You are as much what others think of you as what you think of yourself, in this case.