# Abstract Algebra: Question About the Elements in U(n)

by Shoney45
Tags: abstract, algebra, elements
 P: 366 Here's one way to look at it. In the integers, the equation x2 = 1 has two solutions, namely 1 and -1. Well, this is actually true in U(n) as well, since U(n) is really the multiplicative group $(\mathbb{Z}/n\mathbb{Z})^{\times}$. So how do you write -1 in $\mathbb{Z}/n\mathbb{Z}$?