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Math Help - If A^2 = -I then prove...

  1. #1
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    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
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Hints :

    1) (\det A)^2=(-1)^n

    2) If \lambda \in\mathbb{R} is an eigenvalue of A , then Ax=\lambda x for some 0\neq x\in \mathbb{R}^n .

    Prove that (\lambda^2+1)x=0 (contradiction).

    3) No hint, try it.


    Fernando Revilla
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