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Let A be an n x n matrix such that A^3 = On

  1. May 5, 2009 #1
    I have a problem.
    Let A be an n x n matrix such that A^3 = On (On is a n x n zero matrix). Show that the only possible eigenvalue for A is 0.
     
  2. jcsd
  3. May 5, 2009 #2

    jbunniii

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    Re: Eigenvalue

    An eigenvalue lambda must satisfy

    Ax = lambda x

    for some nonzero vector x.

    Now multiply both sides of the above equation on the left by A, twice, and substitute lambda x in place of Ax where appropriate.

    What is the resulting equation, and what does it imply about lambda?
     
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