There's a Lemma concerning properties of rings I have to prove.

Prove the following properties of a ring $\langle R; +,-,0,\cdot,1\rangle$ and $a,b \in R$:

> 
> (i)$\hspace{2.98em}0a=a0=0$.  
> 
>  (ii)$\hspace{2.7em}(-a)b=-ab$.  
> 
>  (iii)$\hspace{2.5em}(-a)(-b)=ab$.  
> 
>  (iv)$\hspace{2.55em}$ If $R$ is non-trivial (i.e., if it has more than one element), then $1≠0$.
> 
> 
> 

The exercises says that I'm allowed to use the statement (i) without proof.

**My attempt for (ii):**  

Assumption 1 is in R:  

$(-1)(-1) + (-1) = 0 = (1) + (-1)$ which is $(-1)^2 = (1)$?
Is that even a proof?

I don't know about the other statements though.

Thanks I advance. I really appreciate it.