Show that SO(n) is a normal subgroup of O(n)
Solution 1:
Simply note that $SO(n)$ is the kernel of the group homomorphism $$ \det :O(n) \longrightarrow \mathbb{R}^* \ \ \ \ \ A \mapsto \det A$$
Recall that every kernel is a normal subgroup.
Show that SO(n) is a normal subgroup of O(n)
Solution 1:
Simply note that $SO(n)$ is the kernel of the group homomorphism $$ \det :O(n) \longrightarrow \mathbb{R}^* \ \ \ \ \ A \mapsto \det A$$
Recall that every kernel is a normal subgroup.