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Homework Statement
Let a,b,c,d be elements of a group G and let ab = c, bc = d, cd = a, da = b. Examine the expression da^2b and first derive an expression for b in powers of a. Then express c and d in powers of a. Show that a^5 = e (identity element)
Homework Equations
The Attempt at a Solution
So I've been banging me head against this one for a while now. I feel like its something simple and obvious but i can't figure it out. I have an expression for b:
da^2b = daab = (da)(ab) = bc = d
d^-1*daab=d^-1*d
eaab = e
b = a^-2
I can't figure out c or d, well i should say I have worked out values for c and d but know them to be wrong because I can't show a^5 = e. (and also I have the answers to this question)
Thanks