Let $\mathcal A$ be a commutative, unital Banach algebra. Take $A \in \mathcal A$ such that $A$ is non-scalar, i.e. $A\neq \alpha \mathbb I $, where $\mathbb I$ is the unit element. Denote the spectrum of $A$ as $\sigma(A)$ and take $\lambda \in \sigma(A)$.
Why is is the following true?
$$\vert \vert (A-\lambda \mathbb I)B - \mathbb I \vert \vert \geq 1, \forall B \in \mathcal A$$