Group Theory

[munday63]

Hi all,

Can anyone help explain how to begin this question.

Let a and b be elements of a multiplicative group G. Show that there exists a unique element (x which exists in G) such that ax=b.

Thanks

[bilm_ks]

Exists : a(a' b) = (aa')b = eb = b so for x = a'b is ax = b
Unique : Let x2 belongs to G and ax2 = b with x2 <> x.
Then ax = ax2 -> a'(ax) = a'(ax2) -> (a'a)x = (a'a)x2 -> ex = ex2 -> x = x2