Q:

Is the set $SL(2, \mathbb F)$ an Abelian group?

For the set $SL(2,\mathbb F)$, where $\mathbb F$ are entries from either $$\mathbb{Q},\mathbb{R},\mathbb{C} \text{ or } \mathbb{Z}_p \text{  (p is prime)}$$
How should I start by checking this matrix group is an Abelian group?
First off, what is modulo $p$ prime? (modulo integer n is the set of integers in the set smaller than n and relative prime to n so does modulo p prime implies the set of integers which are prime, smaller than n and relative prime to n? Doesn't make much sense to me)

A:

The set $SL(2,\mathbb F)$ is not an abelian group, because  
$$\begin{pmatrix} 
1 & 1\\
0 & 1
\end{pmatrix} 
\begin{pmatrix} 
1 & 0\\
1 & 1
\end{pmatrix}=
\begin{pmatrix} 
2 & 1\\
1 & 1
\end{pmatrix}\ne
\begin{pmatrix} 
1 & 1\\
1 & 2
\end{pmatrix}=
\begin{pmatrix} 
1 & 0\\
1 & 1
\end{pmatrix} 
\begin{pmatrix} 
1 & 1\\
0 & 1
\end{pmatrix}.$$  

