Show that a magma M is associative iff... I have a little trouble showing this... Show that a magma $(M,*)$ is associative if and only if the canonic application $µ$ : $M->End(M)$, $m -> µ(m)$ is a morphism of magma. where $µ(m)$ : $M ->M$, $m'$$->$$µ(m) (m')$ $=$ $m*m'$ Any help/comment is welcome

Since you said in the comment that your main problem is the internal law on $\operatorname{End}(M)$, I'll answer that and leave the rest as an exercise. It is straightforward, but if you have any trouble, feel free to ask.

Suppose you are given $f, g\in\operatorname{End}(M)$. Then the internal law is defined as $(f*g)(m)=(f\circ g)(m)=f(g(m))$