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Here's the question:

Let $D$ be an integral domain. Prove that $D[X]^{\times}=D^{\times}$. (Note: $\times$ is meant to denote an integral domain under multiplication.)

I'm uncertain what the question is asking. Is this equivalent to "Prove that if $D$ is an integral domain, then $D[X]$ is also an integral domain"?

I do apologize if this is the inappropriate place for this question.

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Prove that the only invertible elements of the polynomial ring are the invertible elements of the original ring (canonically embedded into the polynomial ring as constant polynomials). –  Isaac Solomon Dec 4 '13 at 3:39

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