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Suppose A^k=0 for some integer k is greater than or equal to 1

  1. Oct 10, 2009 #1
    I was wondering if anyone could give me some hints on this

    Suppose A^k=0 for some integer k is greater than or equal to 1. Prove that A is not invertible.
     
  2. jcsd
  3. Oct 10, 2009 #2
    Re: Proof

    Try a proof by contradiction. Assume it is invertible with inverse B. Then AB=1. (A^k)B=0B=0
    But B=A^-1. So you can simplify (A^k)B=(A^k)(A^-1)=.....
     
  4. Oct 11, 2009 #3

    HallsofIvy

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    Re: Proof

    Nice!
     
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