Characterizing spectral radius using invertible elements in unital $C^*$ algebra [duplicate]

Consider $$A$$ a unital $$C^*$$ algebra, I want to show that the spectral radius $$r(a)$$ satisfies the following: $$r(a) = \inf_{b\in \operatorname{Inv}(A)}\|bab^{-1}\|$$ where $$\operatorname{Inv}(A)$$ is the set of invertible elements in $$A$$.

So far I can only see one direction, namely $$r(a) \leq \inf_{b\in \operatorname{Inv}(A)}\|bab^{-1}\|$$. I wondering how to prove the other direction.

Thank you very much for the help.