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Math Help - Finding the eigenvalues of a matrix

  1. #1
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    Finding the eigenvalues of a matrix

    Let A be a square matrix of real numbers whose eigenvalues are positive integers.
    It is given that |adj(adj(A))| = 81.
    What is the characteristic polynomial of the matrix?
    --------------------------------------------------

    What I did was this:

    |adj(adj(A))| = |adj(A)|^(n-1) = |A|^(n-1)^2 = 81

    But I don't know how to proceed.
    Any suggestions? Or if there's any other possible way...
    Thanks!
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  2. #2
    Super Member girdav's Avatar
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    Re: Finding the eigenvalues of a matrix

    The determinant of A^{n-1} is either -9 or 9.
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  3. #3
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    Re: Finding the eigenvalues of a matrix

    How do I conclude that?
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  4. #4
    Super Member girdav's Avatar
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    Re: Finding the eigenvalues of a matrix

    Its square is 81.
    Thanks from loui1410
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