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(C) Let $C = A \cap B$. Since $A$ and $B$ have $n$ elements in common,the set $C$ has $n$ elements.We know that $(A 	imes B) \cap (B 	imes A) = (A \

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$n^{2}$

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(C) Let $C = A \cap B$. Since $A$ and $B$ have $n$ elements in common,the set $C$ has $n$ elements.We know that $(A 	imes B) \cap (B 	imes A) = (A \cap B) 	imes (B \cap A)$.Substituting $C = A \cap B$,we get $(A 	imes B) \cap (B 	imes A) = C 	imes C$.The number of elements in $C 	imes C$ is given by $n(C) 	imes n(C) = n 	imes n = n^{2}$.Therefore,the number of elements common to $A 	imes B$ and $B 	imes A$ is $n^{2}$.

If $A$ and $B$ have $n$ elements in common,then the number of elements common to $A \times B$ and $B \times A$ is

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