Does P(A|B)=P(A) imply P(B|A)=P(B)? Please prove your answer.

I know that the answer is yes (my professor stated so in class). Yet I'm struggling to prove how it is so. I can prove how P(A|B)=P(A) for independent events A and B, yet I don't know how to use that knowledge to prove P(B|A)=P(B).

Thanks for any help!