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Prove or Disprove these statements on matrices!

  1. Mar 3, 2009 #1
    1. The problem statement, all variables and given/known data

    Prove or disprove the following statements concerning 2 x 2 matrices.

    (a) If A^3 = 5I then A is invertible.
    (b) If A and B are both invertible then AB - BA is not invertible.
    (c) If ABC = I then B is invertible.
    (d) If A^2 - 3A -2I = 0 then (A-1) and (A-2I) are both invertible.
    (e) If A= EB and E is elementary then B = FA for some elementary F.

    2. Relevant equations

    I am a little confused on the following:
    What is I?
    How would I go about proving or disproving any of these, since it depends on the system of vectors in a particular matrix...can I simply do a generic matrix to prove/disprove the statement? Like using constants like a, b, c...etc...?

    In most cases I know what to do, I just have trouble understanding what the question wants...exactly...

    3. The attempt at a solution

    Thank you!
  2. jcsd
  3. Mar 3, 2009 #2
    I would assume, without further info, that I is the identity matrix. A lot of times when you are proving statements concerning matrices, the identity matrix plays a key role. It's been a while since I've done Linear Algebra so I can't really say anymore about it. Hope this helps!
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