'Shouldn't the candidate key be AX not A?

In my study documents I found the following relation with functional dependencies:

R = {A,B,C,D,E,X}
F = {A → B, A → C, C → B, C → D, D → E}

The solution says that the only key candidate is A and that the relation is in 2NF.

Shouldn't the candidate key be AX? And if that's the case, wouldn't the relation only be in 1NF because B isn't fully functionally dependent on AX?

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