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A Level P6 exam

  1. Jun 3, 2003 #1
    I was revising for my ALevel P6 exam the other day and I came up against a very tough question...

    I can do parts i and ii

    axa = x^-1, let x = e
    a^2 = e
    a = a^-1

    for part ii

    axa = x^-1
    axax = e
    axax(ax)^-1 = (ax)^-1 //ax and (ax)^-1 will cancel
    ax = (ax)^-1

    but for part iii and iv I seem do always go around in circles or i end up with something obvious like x = x. Unfortunately there aren't any answers to this question.

    ps: I hope this was the correct place to post this, i had a look in the homework help section but it was mostly about physics. :s
    And i have already taken the exam now but the question is kinda bugging me.

    Thanks in advance for any help

    Jim
     
    Last edited by a moderator: Feb 5, 2013
  2. jcsd
  3. Jun 3, 2003 #2

    Hurkyl

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    Gold Member

    The result of part two is the key to solving answer three. Maybe if I slightly restate what you've proven, the way to go might become apparent:

    Theorem: for all y, (ay) = (ay)^-1

    Goal: prove x=x^-1 for all x


    And result 4 follows from a few applications of rule 3 and the identity:
    (xy)^-1 = (y^-1)(x^-1)
     
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