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Matrix operation question

  1. Aug 19, 2009 #1
    1. The problem statement, all variables and given/known data

    Matrix A and B are both square matrices of the same size.

    Is it possible to compute,

    AB^2009

    If not, why not?


    3. The attempt at a solution

    Just had this question in an exam, the exam did not allow calculators and I could not answer this question, I gather it is not possible but I cannot explain why.

    Because A and B are square matrices it is possible to multiply them together but I am unsure about the exponent. Any ideas?
     
  2. jcsd
  3. Aug 19, 2009 #2

    CompuChip

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    Suppose that A and B are both n x n matrices. Then what is the size of AB? Then what about ABB = AB^2? And ABBB = AB^3? ...
     
  4. Aug 19, 2009 #3
    Well if A and B are both n x n then they will always be n x n matrices. So does that mean that it is possible?
     
  5. Aug 19, 2009 #4

    HallsofIvy

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    By the way, is that AB2009[/b] or (AB)2009?

    It doesn' really matter. The only important point is that any two n by n matrices can be multiplied and give an n by n matrix as a result- which can be multiplied again by any other n by n matrix.
     
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