# Element Commutes with Square in Group/Proof 1

## Theorem

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

Let $x \in G$.

Then $x$ commutes with $x \circ x$.

## Proof

 $\displaystyle x \circ \left({x \circ x}\right)$ $=$ $\displaystyle \left({x \circ x}\right) \circ x$ Group Axioms: $G1$: Associativity

$\blacksquare$