Identify the false statement.

• A

  A non-empty subset $H$ of group $G$ is a subgroup of $G$ if and only if for every a, $b \in H \rightarrow a * b^{-1} \in H$
• B

  The intersection of two subgroups of a group $G$ is again a subgroup.
• Correct answer
  C

  A group of order three is not abelian
• D

  If in a group $F,(a b)^{2}=a^{2} b^{2}, \forall a, b \in G$ then $G$ is abelian

Hence, the correct answer is option: 'C'.