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6. Let (G, *) be a group. Show that each equation of either the form ax = b or the form xa = b has a unique solution in G.
7. Show that (R - {1}, *), where a * b = a + b + ab is a group
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6. Let (G, *) be a group. Show that each equation of either the form ax = b or the form xa = b has a unique solution in G.
7. Show that (R - {1}, *), where a * b = a + b + ab is a group
[Recall:
Let G is a non-empty set, A binary operation * together with G defined as (G,*) is called a "Group" if the following properties hold in G:
G1: Closure property:
a * b G for each a G and b G
G2: Associative property:
a*(b*c) = (a*b)*c for each a G, b G and c G
G3: Existence of identity element:
a*e = e *a = a , e is the identity element in G.
G4: Existence of inverse element:
For each a G, there exists an ...
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