Clarification on Symmetry Group My text says 
"It is a general fact, and an easy one to prove, that the invertible transformations of a mathematical object that preserve some feature of its structure always form a group.  We call this group the symmetry group of the object."
My question is why is this so?  How do we know that such transformations are associative?

Invertible transformations are bijective functions and we know 
$$ (f \circ g) \circ  h = f \circ ( g \circ h ) $$ 
if $f,g,h$ are bijective.
