Question

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

• A. $n$
• B. $2n$
• C. $n^2$
• D. $0$

Answer 1

Answer: (C)

$n^2$

If there are $m$ elements in $A$ and $m$ elements in $B,A\times B$ and $B\times A$ both will be having $m^2$ elements.

Since there are $n$ elements common to $A$ and $B$, there will be $n^2$ such pairs in $A\times B$ and $B\times A$, which will have both the elements same.

Since the elements are same, they are commutative and hence there will be $n^2$ elements common to $A\times B$ and $B\times A$