For an abelian group: (A) commutator $[a,b]=aba^{-1}b^{-1}=e$ ✓ (true for abelian); (C) $G' = \{e\}$ (derived subgroup is trivial) ✓; (D) $Z(G)=G$ (every element commutes) ✓. Statement (B) '$G$ is a simple group of order 60' is NOT necessarily true — the simple group of order 60 is $A_5$, which is non-abelian. An abelian simple group has prime order, not order 60.