You're being dishonest. The question is not whether or not "A is A," but whether we can accept it as an axiom. Unless you're prepared to give us a means of knowing what A is, then you can't accept it as an axiom, either.
Actually, "A is A" is almost a circular argument because it does not require you define either. Because the very point is that "this thing" is "this thing".
You define it by itself. That is the whole point.
And if you have trouble with such a simple concept, I'm not sure what the point of this conversation *is*.