Let $A\in M_n(C)$ satisfy $||Ax||\leq ||x||$ for all $x\in C^n$. Then prove that if $k \in C$ such that $|k|>1$, then $A-kI$ is invertible.

Question

Let $A\in M_n(C)$ satisfy $||Ax||\leq ||x||$ for all $x\in C^n$. Then prove that if $k \in C$ such that $|k|>1$, then $A-kI$ is invertible.

suppose $(A-kI)(x)=0$

I want to show $x=0$

I am really unable to think of a way to connect this with $||Ax||\leq ||x||$

Please help.