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Math Help - Abstract Algebra

  1. #1
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    Abstract Algebra

    G is a group. Suppose a in G is the unique element of order 2. Show that ax=xa for all x in G. Start by showing that xax^(-1) has order two.

    No idea where to start for this one.
    Thanks in advance.
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  2. #2
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    Quote Originally Posted by fulltwist8 View Post
    G is a group. Suppose a in G is the unique element of order 2. Show that ax=xa for all x in G. Start by showing that xax^(-1) has order two. No idea where to start for this one.
    Why is that the case?
    \left( {xax^{ - 1} } \right)\left( {xax^{ - 1} } \right) = ?
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  3. #3
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    (xy)^2 = e so xyxy = e so xy=yx
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