Thread: binary relation

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 = { }

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.

Hello, riptorn70!

Welcome aboard!

I have the following set

p,q)\!:\;p,q \in \Re,\;p^2-q^2 \neq 0 " alt="A \:= \p,q)\!:\;p,q \in \Re,\;p^2-q^2 \neq 0 " />}

Define * on by: . pr+qs, ps+qr)" alt="(p,q) * (r,s) \:= \pr+qs, ps+qr)" />

Show that * is a binary operation on
In other words , that is closed and that * is associative.

We have: .

Since is closed under multiplication and addition,
. . Hence, is closed.


Is * associative?
Does ?

Left side: .
. . . . . .
. . . . . .

Right side: .
. . . . . . .
. . . . . . .

They are equal . . . the operation is associative.

Many thanks soroban for your answer. It is much appreciated. Riptorn70.