Shaik transitive dependency occurs when a non prime attribute is transitively dependent on the key right?

So if B->A is a valid FD in a relation R (A,B,C) where the FDs A->B and B->C also hold, then both A and B become candidate keys for the relation R and so B->C is no longer a transitive dependency right?

A functional dependency X->Y is said to be in 3NF if either X is a superkey or Y is a prime attribute.

So following this above definition, B->C no longer violates this rule as B is a superkey if B->A hold on relation R.

But in the absence of B->A, then neither B is a superkey nor C is a prime attribute. So the relation R wont be in 3NF then.

am i right Shaik?