# Math Help - Prove that [1] and [p-1] are their own multiplicative inverses

1. ## Prove that [1] and [p-1] are their own multiplicative inverses

Let p be a prime integer. Prove that [1] and [p-1] are the only elements in Zp that are their own multiplicative inverses.

2. Originally Posted by rainyice
Let p be a prime integer. Prove that [1] and [p-1] are the only elements in Zp that are their own multiplicative inverses.
Is this supposed to be done group theoretically or number theoretically?

3. Originally Posted by Drexel28
Is this supposed to be done group theoretically or number theoretically?
i think it is group because this problem is in the congruence classes section. thanks