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]