Exercise 3, § 3

Let $V$ be a finite dimensional real vector space and $W$ a finite subgroup of $\mathbf{GL}(V)$ generated by reflections. Show that every element of order 2 of $W$ is a product of pairwise commuting reflections belonging to $W$. (Argue by induction on $\dim(V)$, and use Prop. 2.)

(6) This exercise, hitherto unpublished, was communicated to us by R. Steinberg.