## In a unital ring, (-1)² = 1

Let $R$ be a ring with 1. Show that $(-1)^2 = 1$ in $R$.

Let $x \in R$. Then $(-1)^2x = (-1)(-x) = x$. Similarly, $x(-1)^2 = (-x)(-1) = x$. By the uniqueness of 1, $(-1)^2 = 1$.