 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ii/paper-1/19i/b/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Put

A = (0 ε ε 0), B = (ω 0 0 ω^{2}) .

Then

A^{2} = ε^{2} I

, so

A^{2 n} = I

because

ε^{2 n} = 1

, and

B^{3} = I

. Moreover,

A

exchanges the two eigenspaces of

B

A^{- 1} B A = B^{- 1} .

The matrices therefore satisfy every defining relation of

G_{6 n}

 New to topics? Read the docs here!