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In^-1=In Lin alg

  1. Mar 29, 2009 #1
    1. The problem statement, all variables and given/known data

    In^-1=In
    proof that!

    2. Relevant equations
    1 0
    0 1
    = I2^-1= I2 for an example.
     
  2. jcsd
  3. Mar 29, 2009 #2
    The inverse matrix [tex]A^{-1}[/tex] of [tex]A[/tex] is by definition the matrix such that [tex]A^{-1}A=I_n[/tex] and [tex]AA^{-1}=I_n[/tex]. So is [tex]I_n[/tex] the inverse of [tex]I_n[/tex]?
     
  4. Mar 29, 2009 #3
    yes In is the inverese of In because In^-1 is the inverse of In and In^-1=In
    true?
     
  5. Mar 29, 2009 #4
    anyone?
     
  6. Mar 29, 2009 #5
    Just use the definition. You want to check that the inverse of [tex]I_n[/tex] is [tex]I_n[/tex] itself (this is just another way of saying [tex]I_n^{-1}=I_n[/tex]). What it comes down to is that [tex]I_nI_n=I_n[/tex].
     
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