Infinite group with cofinite topology is not a topological group

Statement
Let $$G$$ be an infinite group. Equip $$G$$ with the cofinite topology. With this topology, $$G$$ is not a disproves property satisfaction of::topological group.

Proof
Given: An infinite group $$G$$ equipped with the cofinite topology.

To prove: The multiplication map $$G \times G \to G$$ is not continuous where $$G \times G$$ is equipped with the product topology.

Proof: