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.