1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Compute the determinant of ##A##.
  5. Oct 27, 2015 #4
    I took me a while but I got it. Thanks both of you!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted