Why is d4 not abelian?

Could you please elaborate on why the group d4, often referred to as the dihedral group of order 8, is not considered abelian? It's my understanding that in an abelian group, the order of multiplication doesn't matter, i.e., for any two elements a and b in the group, a * b = b * a. However, with d4, which comprises rotations and reflections of a square, it seems the order in which we apply these transformations can yield different results. Could you explain why this property disqualifies d4 from being abelian?