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Homework Help: Identity matrix

  1. Feb 18, 2010 #1
    1. The problem statement, all variables and given/known data

    let I_n be as an identity matrix where a_ij = 1 when i=j
    I just want to ask that is it true that all identity matrix has an inverse (determinant is not 0) for n>=2?



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 18, 2010 #2

    CompuChip

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    The determinant of In is 1, as you can easily compute (expanding along any row or column, you find that det(In) = 1 . det(In - 1) and clearly det(I1) = 1).

    Also it is invertible, and it is its own inverse. You can check this directly from the definition.
     
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