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

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- Feb 3rd 2011, 11:09 PMhashshashin715If 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 - Feb 4th 2011, 12:35 AMFernandoRevilla
:__Hints__

**1)**

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

Prove that (contradiction).

**3)**No hint, try it.

Fernando Revilla