Group is Quasigroup

Theorem
Let $\left({G, \circ}\right)$ be a group.

Then $\left({G, \circ}\right)$ is a quasigroup.

Proof
By the definition of a quasigroup it must be shown that:


 * $\forall g \in G$ the left and right regular representations of $\lambda_g$ and $\rho_g$ are permutations on $G$.

This follows immediately from Regular Representations in Group are Permutations.