Let $R$ be a commutative ring and define $$B = \{ f = \sum_{n=0}^{\infty} a_n X^n: a_n \in R\}$$ where $X$ is an indeterminate over $R$.

a. Show that $B$ is a ring.

b. Prove or disprove: $f$ is a unit if and only if $a_0$ is a unit.

I could not relate this question with the post Characterizing units in polynomial rings exactly since there is nothing about nilpotent elements. Maybe I need a more detailed explanation.