$\pi_1(X,x_0)$ is a group with respect to the product $[f][g]=[f.g]$
satisfy three properties
$1. $Associative
$2.$ Identity
$3.$Inverse
My question : How to show the associative properties in $\pi_1(X,x_0)?$
My attempt : I was reading the Allen Hatcher book but im not understand fully
In Allen book it is written that given $3$ path $f,g,h$ with $f(1)=g(0)$ and $g(1)=h(0)$ implies $(f.g).h=f(g.h)$
Actually i don't understand the Allen book because he doesn't explain in detail that why $(f.g).h=f(g.h)?$