Griffiths Introduction to Elementary Particles · Problem 4.5
Bound States — David J. Griffiths
Physics — QFT · matrix-groups
Problem
(a) Show that the set of all unitary n×n matrices constitutes a group. (To prove closure, for instance, you must show that the product of two unitary matrices is itself unitary.)
(b) Show that the set of all n×n unitary matrices with determinant 1 constitutes a group.
(c) Show that O(n) is a group.
(d) Show that SO(n) is a group.