3.I.2E

What is the orthogonal group $O(n)$ ? What is the special orthogonal group $S O(n) ?$

Show that every element of the special orthogonal group $S O(3)$ has an eigenvector with eigenvalue 1 . Is this also true for every element of the orthogonal group $O(3)$ ? Justify your answer.

*Typos? Please submit corrections to this page on GitHub.*