Question

How many elements in a AxB and BxA are commom if n elements are common to A and B

Answer 1

${n}^{2}$
This is the answer. l hope it will help you.

Answer 2

The Cross Product of A and B is

A × B = {(a,b) : a∈A and b∈B}     and   B × A = {(b,a) : a∈A and b∈B}

if (A∩B) = n then

n elements of A will have cross product with n elements of B

which will form $n^2$ coordinates

so in Set of (A × B) ∩ (B × A) there will be $n^{2}$ elements