The following statement popped up on a review sheet for an exam I have coming up. I understand the statement but am unsure how to prove it. I'm also a little unsure about how invertibility works in polynomials. Any sources about the proof or inverting polynomials would be great, thanks!
All non-zero elements of $\mathbb{F}_p[x]/(h(x))$ are invertible iff $h(x)$ is irreducible