Hi.

I need to prove or disprove the following:

1. Let $\displaystyle B=\left \{ s+tx|s,t\in \mathbb{Q} \right \}$ and $\displaystyle A=B\setminus \left \{ 0+0x \right \}$. A is a Group.

2. Let $\displaystyle B=\left \{ s+tx|s,t\in \mathbb{Z}_5 \right \}$ and $\displaystyle A=B\setminus \left \{ 0+0x \right \}$. A is a Group.

both with the operation:

$\displaystyle (s+tx)*(u+vx)=(su+2vt)+(sv+tu)x$

My intuition says 1 is true and 2 is false (the unit element in 1 is $\displaystyle (1+0\cdot x)=1$, and with simple algebra I can find the inverse element for a given element $\displaystyle (s+tx)\in A$), but I'm not sure about 2.

Can someone please give me some help with it?

Thanks in advanced!