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Homework Help: Linear algebra

  1. Feb 25, 2010 #1
    1. The problem statement, all variables and given/known data

    state if the statement if it's true or false (give a brief explanation if it's true or give a counter example if it's false)

    2. Relevant equations
    If A is an invertible nxn matrix, then A^m is not equals to O_m,n for all natural m


    3. The attempt at a solution
    what is O_m,n?
     
  2. jcsd
  3. Feb 25, 2010 #2

    CompuChip

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    I presume it would be the zero matrix (the unique m x n matrix all whose entries are 0).
     
  4. Feb 25, 2010 #3

    HallsofIvy

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    In other words, if A is an invertible matrix, is it possible to have [itex]A^n= 0[/itex] for some n? Start multiplying both sides of [itex]A^n= 0[/itex] by [itex]A^{-n}[/itex]. "Repeat as needed".
     
  5. Feb 25, 2010 #4

    CompuChip

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    I would choose another approach, where the hint "consider the determinant" applies.

    Take your pick :)
     
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