A.

B.aba=1

To investigate whether the first one is possible, think of some small groups and try and find a and b with a^2 = b^2 and ab =/= ba.

For the second, manipulate the equation aba = 1 and see what happens.

For the second, manipulate the equation aba = 1 and see what happens.

Oh thanks! I see the second one now.

vonLipwig wrote:To investigate whether the first one is possible, think of some small groups and try and find a and b with a^2 = b^2 and ab =/= ba.

For the second, manipulate the equation aba = 1 and see what happens.

Excellent. What did you get?

For the first one, try the symmetric group S_3.

For the first one, try the symmetric group S_3.

yes. Coz ab=ab(aba)=(aba)ba=ba if aba=1

and S3 is a brilliant idea! thanks!

and S3 is a brilliant idea! thanks!

Yep! Good work =)

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