Use Corollary 2 of Lagrange’s Theorem (Theorem 7.1) to prove that the order of U(n) is even when n> 2.
Reference:
Theorem 7.1 Lagrange’s Theorem†: |H| Divides |G|
If G is a finite group and H is a subgroup of G, then |H| divides |G|. Moreover, the number of distinct left (right) cosets of H in G is |G| /|H|.
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