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7. Show that if abab = aabb, then it must be that ab = ba.
a' is inverse for a
b' is inverse for b
e is identity
abab = aabb
(abab)b' = (aabb)b'
(aba)(bb') = (aab)(bb')
(aba)e = (aab)e
aba = aab
a'(aba) = a'(aab)
(a'a)(ba) = (a'a)(ab)
e(ba) = e(ab)
ba = ab
ab = ba
7. Show that if abab = aabb, then it must be that ab = ba.
Stars (operation symbols) are missed in between these letters.
Show that a group can have one and only one identity e. There should not be 2 different identities e1 and e2 in the same group, when e1 does not equal e2.
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