Let, $G$ be a subgroup of $GL_n(\Bbb{C})$. Prove that, $\exists$ an inner product on $\Bbb{C}^n$ such that $G\subset U_n$

Question

Here, $U_n$ denotes the set of unitary matrices in $GL_n(\Bbb{C})$ i.e. $U_n=\{A\in GL_n(\Bbb{C})|AA^*=A^*A=I\}$
We have to find an inner product $\langle,\rangle$ on $\Bbb{C}^n$ .
I have to prove that $G\subset U_n$ i.e. $\forall A\in G$ we must have $\langle Ax,Ay\rangle=\langle x,y\rangle$ (This is an equivalent definition of the unitary matrix).
There is a hint provided in the book-
We can define a group action $G\times \Bbb{C}^n\to\Bbb{C}^n$ by $(A,v)\mapsto Av$
This group action can help you to get this $\langle,\rangle$.
But I don't have any idea how to proceed from here. Can anyone help me solve the problem? Thanks for the assistance in advance.