Question:
Prove that $A \times B=B \times A \Rightarrow A=B$.
Solution:
Let A and B be any two sets such that
$A \times B=\{(a, b): a \in A, b \in B\}$
Now,
$B \times A=\{(b, a): a \in A, b \in B\}$
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
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