Finding determinant given determinant of another matrix

  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,
  2. jcsd
  3. rock.freak667

    rock.freak667 6,219
    Homework Helper

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

    So if you factor A^2-3A you can use det(A-3) = 2
  4. so

    A^2 -3A = 2I factors to


    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. rock.freak667

    rock.freak667 6,219
    Homework Helper

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