Let A and B be any two sets such that

A × B = {(a, b): a ϵ A, b ϵ B}

Now,

B × A = {(b, a): a ϵ A, b ϵ B}

A × B = B × A

(a, b) = (b, a)

We can see that this is possible only when the ordered pairs are equal.

Therefore,

a = b and b = a

Hence, Proved.