How to prove that End(R) is isomorphic to R? I tried to prove this: 
$R$ as a ring is isomorphic to $End(R)$, where $R$ is considered as a left $R$-module. The map of isomorphism is
$$F:R\to End(R), \quad   F(r)=fr,$$ 
where $fr(a)=ar$. And I define the multiplication in $End(R)$ by $(.)$, where $h.g=g\circ h$ for $g,h$ in $End(R)$. 
Is this true?

Hint: Let $F\in End(R)$. Put $a:=F(1)$, show that $F(x)=xa, \forall x\in R$.
