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Show that if a is any m x n matrix, then ImA = A and AIn = A

  1. Oct 7, 2009 #1
    1. The problem statement, all variables and given/known data

    Show that if A is any m x n matrix, then the m x m identity multiplied by A = A, and A multiplied by the n x n identity = A.

    2. Relevant equations



    3. The attempt at a solution

    I know how to prove this by writing out a general m x n matrix, and multiplying it by the identity, but is there a better way of showing this? It just seems kind of silly when I write it out...
     
  2. jcsd
  3. Oct 7, 2009 #2
  4. Oct 7, 2009 #3
    I can`t really think of another way. The cleanest way I can think of:

    [tex] (AI)_{i,j } = \sum_{r= 1}^n A_{i, r} I_{r, j} = a_{i, j} [/tex]
     
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