Past exam of the mathematics course of the University of Cambridge / 2015 / ii / Paper 1 / 15F / b / i

Call the two proposed matrices $A$ and $B$. Direct multiplication gives $A^{2n}=I$, $B^2={ϵ}^{n}I=A^n$, and $B^{-1}AB=A^{-1}$. Both are invertible since $ϵ\ne 0$. They therefore satisfy every defining relation, and the universal property of a group presentation gives the desired group representation.