Proving R[x] is a Principal Ideal Domain Implies R is a Field

[Fizzicist]

Homework Statement

Let R be an integral domain and suppose that R[x] is a principal ideal domain. Show that R is a field.

Homework Equations

I don't know where to start, I'm not familiar with this material. I was browsing through an abstract algebra book and found this. Would like an explanation of what it means, thank you.

The Attempt at a Solution

 

[HallsofIvy]

The difference between an integral domain and a field is that every non-zero member of a field has a multiplicative inverse. That is what you need to prove.

(If you are not familiar with the material, why are you trying to do this problem? Wouldn't it be better to start at the beginning and read the book rather than "browsing"? Do you need definitions of "field" and "integral domain"?)