Order of Finite Abelian Group with p+ Order p Elements is Divisible by p^2/Examples/Order 3

Example of Order of Finite Abelian Group with $p+$ Order $p$ Elements is Divisible by $p^2$
Let $G$ be a finite abelian group whose identity is $e$.

Let $G$ have more than $2$ elements of order $3$.

Then:
 * $9 \divides \order G$

where:
 * $\divides$ denotes divisibility
 * $\order G$ denotes the order of $G$.