Show that $f (x) = ax + 1 \in R[x]$ is invertible in $R[x]$.

Question

Let $R$ be a commutative ring with unit. Consider $a ∈ R$ such that $a^2 = 0$. Show that $f (x) = ax + 1 \in R[x]$ is invertible in $R[x]$.

I have no idea how to do it, can you give me any tips?

Answer 1

Hint: $(ax+1)(1-ax) = 1-a^2x^2 = 1$.