Number of common elements in $A \times B $ and $B \times A$

Question

This question was part of maths worksheet of my brother and I was unable to solve it. He studies in High Shcool.

So, I am asking for help here.

Let there are 5 common elements between A and B set. Then what is the number of common elements in $A \times B $ and $B \times A$ ?

Although this question seems to be of basic Sets and relation but I am clueless on how to approach this despite being an bachelor student of mathematics myself .

So, CAn you pleaese help me on how should I aproach this question .

Thanks!!

Answer 1

Hint Show that $(x,y) \in A \times B \cap B \times A$ if and only if $x,y \in A \cap B$.