Group has Latin Square Property/Proof 4

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

Then $G$ satisfies the Latin square property.

That is, for all $a, b \in G$, there exists a unique $g \in G$ such that $a \circ g = b$.

Similarly, there exists a unique $h \in G$ such that $h \circ a = b$.

That is, these equations have unique solutions in $G$.

Proof
We shall prove that this is true for the first equation:

Conversely:

The proof that the unique solution of $h$ is $b \circ a^{-1}$ in the second equation follows similarly.