Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Matrix Similarity Proof - need someone to check if it's correct

  1. Feb 18, 2010 #1
    1. The problem statement, all variables and given/known data
    My textbook has no answers so I was wondering if someone could let me know if I'm right.

    The question: A and B are m x n matrices.
    Let A = I. Find when B = A.


    2. Relevant equations



    3. The attempt at a solution
    What I did seems too easy:

    If B ~ A, then A ~ B (this is just a property of similarity)

    Since A = I, we can sub in for A

    So B = A

    Did I just argue myself in circles?
     
    Last edited: Feb 18, 2010
  2. jcsd
  3. Feb 18, 2010 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    That's fine. You can take the 'I' out because IP=P. 'I' is the identity matrix.
     
  4. Feb 18, 2010 #3
    Great, thank you! Do you think it's necessary to show that if A ~ B, B ~ A?
     
  5. Feb 18, 2010 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    If you're not clear on why it's true, you should probably show it. It's easy enough.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook