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Matrix property proof

  1. Oct 27, 2015 #1
    1. The problem statement, all variables and given/known data
    Show that no matrix A ∈ M3 (ℝ) exists so that A2 = -I3

    2. Relevant equations


    3. The attempt at a solution
    This is from a french text book of first year linear algebra. I'm quite familiar with properties of matrices but I don't have any idea of how to prove this.

    Thanks for the help!
     
  2. jcsd
  3. Oct 27, 2015 #2

    andrewkirk

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    Think about the determinants in the given equation.
     
  4. Oct 27, 2015 #3

    fzero

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    Compute the determinant of ##A##.
     
  5. Oct 27, 2015 #4
    I took me a while but I got it. Thanks both of you!
     
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