Spectral radius of an invertible element in a Banach algebra.

Question

Let $A$ be a commutative Banach Algebra. Suppose $a\in A$ is invertible and $r(a)=\|a\|$, then is $r(a^{-1})=\|a^{-1}\|$, where $r$ denotes the spectral radius?

Answer 1

Say $K=\{0,1\}$, with the discrete topology. Let $A=C(K)$, but with the non-standard norm $||f||=\max(|f(0)|,2|f(1)|)$.