1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    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!

Linear Algebra: Find A for a 2x2 matrix and when A^1001 = I

  1. Apr 18, 2013 #1
    1. Find A, a 2x2 matrix, where [itex]A^{1001}=I_{2}[/itex]


    2. I know that that if [itex]A^{2}=I_{2}[/itex], then A is either a reflection or a rotation by π.



    3. If I use advantage of that fact that A in [itex]A^{2}=I_{2}[/itex] is a rotation by π then I know that [itex]A^{1001}=I_{2}[/itex] is true when A is a rotation by [itex]2π/1001[/itex]

    Is there any other way to do this problem or is it only solvable by considering the fact that A is a rotation. Can you do it by considering A to be a reflection?
     
  2. jcsd
  3. Apr 18, 2013 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You said it yourself. A reflection satisfies A^2=I. How can one satisfy A^1001=I?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Linear Algebra: Find A for a 2x2 matrix and when A^1001 = I
Loading...