Center of Opposite Group

Theorem
Let $\struct {G, \circ}$ be a group.

Let $\struct {G, *}$ be the opposite group to $G$.

Let $\map Z {G, \circ}$ and $\map Z {G, *}$ be the centers of $\struct {G, \circ}$ and $\struct {G, *}$, respectively.

Then:


 * $\map Z {G, \circ} = \map Z {G, *}$

Proof
We have, for $g \in G$:

Hence the result, by definition of set equality.