Answer : Given: A = B, where A and B are nonempty sets. Need to prove: A × B = B × A
Let us consider, (x, y) (A × B)
That means, x A and y B
As given in the problem A = B, we can write,
⇒ x B and y A
⇒ (x, y) (B × A)
That means, (A × B) ⊆ (B × A)—- (1)
Similarly we can prove,
⇒ (B × A) ⊆ (A × B)—- (2)
So, by the definition of set we can say from (1) and (2), A × B = B × A [Proved]