Hello, I am new to this site and I have noticed this is a busy one with some experienced mathematicians. I hope someone can help me with the problem I have. Here it is:

I have the following set A.

A = {$\displaystyle (p,q) : p,q \in \Re,p^2-q^2 \neq 0 $}

Define * on A by (p,q) * (r,s) = (pr+qs, ps+qr)

I need to show that * is a binary operation on A (in other words , that A is closed)

and that * is associative.

Your assistance will be well received,

thankyou.