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Finding determinant given determinant of another matrix

  1. May 11, 2011 #1
    1. The problem statement, all variables and given/known data

    Let A be a 3 x 3 matrix satisfying the equation [tex]A^{2}[/tex]-3A-2I=0 where I is the 3x3 identity matrix. Find det(A) given the det(A-3)=2

    3. The attempt at a solution

    Well cant find anything like this in my textbook, notes or google. I imagine its a pretty simple matrix property i've overlooked but otherwise i have no clue what to do!


    Help much appreciated,
    Ben
     
  2. jcsd
  3. May 11, 2011 #2

    rock.freak667

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    det(AB) =det(A)*det(B)

    So if you factor A^2-3A you can use det(A-3) = 2
     
  4. May 11, 2011 #3
    so

    A^2 -3A = 2I factors to

    A(A-3)=2I

    and using property det(AB)=det(A)det(B)

    det(A)det(A-3)=det(2I) so det(A)=det(2I)/det(A-3)
     
  5. May 11, 2011 #4

    rock.freak667

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    Yes and you can easily find det(2I).
     
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