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Linear algebra question

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

    question 1:
    If A is a matrix satisfying 3A^2+6A-I=0, find the inverse of A.

    question 2:
    Let A be a 3x3 matrix with 4A = A^7. Find the possible values det A.

    2. Relevant equations


    3. The attempt at a solution

    this was a very long homework about 17 questions, i solved the others but i got no clue where to start with these, any help is appreciated.

    Best Regards.
  2. jcsd
  3. Dec 3, 2009 #2


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    Gold Member

    HINT: Multiply through by A-1
    HINTs: det(4A) = 4ndet(A) for an nxn matrix. det(A7) = (det(A))7
  4. Dec 3, 2009 #3


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    Science Advisor

    Or, for question 1, note that [itex]3A^2+ 6A= I[/itex] so [itex](3A+ 6)A= I[/itex].
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