Thread: If A^2 = -I then prove...

Given an n x n matrix A with real entries such that A^2 = -I, prove the following about A:

1) n is even
2) A has no real eigenvalues
3) det A = 1

Hints :

1)

2) If is an eigenvalue of , then for some .

Prove that (contradiction).

3) No hint, try it.


Fernando Revilla