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Another Really Easy Group Calculations which i cant do

  1. Oct 27, 2008 #1
    1. The problem statement, all variables and given/known data
    prove that if aba-1=b2

    then a3ba-3=b8

    3. The attempt at a solution

    Ive tried lots of different things, none of which have worked.

    i trield left and right multiplying by a^2 and a^-2 but couldnt figure it out.

    I know there is some magical trick but i cannot for the life of me figure it out.
     
  2. jcsd
  3. Oct 27, 2008 #2
    There's no real way to give you a hint so I'll just do the first step:

    Note that [tex]ba^{-1}=a^{-1}b^2[/tex] and [tex]ab=b^2a[/tex]

    [tex]a^3ba^{-3}=a^2b^2a^{-2}=aabba^{-1}a^{-1}[/tex]
     
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