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I am trying to prove a simple thing, that if AxA = BxB then A=B.

The intuition is clear to me. If a pair (x,y) belongs to AxA it means that x is in A and y is in A. If a pair (x,y) belongs to BxB it means that x is in B and y is in B. If the sets of all pairs are equal, it means that every x in A is also in B and vice versa.

How do I prove it formally ?

Thank you !