- #1
Jummeh
- 5
- 0
I was revising for my ALevel P6 exam the other day and I came up against a very tough question...
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
I can do parts i and iiG is a multiplicative froup with identity element e, and a is a fixed element of G for which axa = x^-1 for all elements x belonging to G. Prove that...
i/ a = a^-1
ii/ ax = (ax)^-1 for all x belong to G //cant find the little symbol
iii/ x = x^-1 for all x belong to G
iv/ xy = yx for all x, y belong to G
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: