How to find generator of $(G,\ast)?$

Question

Let $G=\{1,2,3,4,5,6,7,8,9,10\}$.

An operator $\ast$ on $G$ is defined by $a\ast b=r$, where $r$ is the remainder when $4ab$ is divided by $11$ for $a,b$ in $G$. (For example $6\ast 9=7$, the remainder when $216$ is divided by $11$.)

What is the generator of $(G,\ast)$? Please explain your answer

Answer 1

Hint: The group $U(11)$ is cyclic of order $10$ and $g=2$ is a generator. How is your group related to $U(11)$?

Reference for finding a generator of $U(p)$ for $p$ prime:

Given a prime p find a generator of $\mathbb{Z}_p ^{*}$