For $n \ge 3$, let $$ Q = \langle x,y \mid x^{2^{n-1}}=e, yxy^{-1} = x^{-1}, x^{2^{n-2}} = y^2 \rangle $$ be the generalized quaternions group.
I want to show that $Q$ has a unique involution using the presentation.
I know that it may be $x$ or $y$ because the only involution in the quaternions (which is $-1$) also lies in the center. In this question it's said that pretty easy but I don't see how to start.
Any hints?