Question: Given three random variables A,B,C, suppose that P(AB)=P(A|C). Is it always true that P(BA)=P(C|A)? If it is always true, please derive it. Otherwise, please give

Given three random variables A,B,C, suppose that P(AB)=P(A|C). Is it always true that P(BA)=P(C|A)? If it is always true, please derive it. Otherwise, please give a counter-example

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