(a) A must be equal to I ?
(b) det A must be equal to 1 ?
(c) In general, if A^n = I, then (a) and (b) are always true ?
Please prove your result.
更新1:
To : Forretrio,自由自在 and doraemonpaul. Appreciate your helps. Forretrio provided answer to (a) although may be incomplete, it is acceptable to me. For (b), 自由自在 showed that det A can be +1 or - 1, but is this the only possible answers? Is this answers also apply to A^n = I ? Please explain, thks.