- #1

U.Renko

- 57

- 1

## Homework Statement

Let [itex]a,b[/itex] be elements of a group [itex] G[/itex]. Show that the equation [itex]ax=b [/itex] has unique solution.

## Homework Equations

none really

## The Attempt at a Solution

[itex]ax = b [/itex]. Multiply both sides by [itex] a^{-1}[/itex]. (left multiplication). [itex] a[/itex] is guaranteed to have an inverse since it is an element of a group.

Then [itex] a^{-1}ax = a^{-1}b[/itex] and therefore the equattion has solution [itex]x=a^{-1}b[/itex].

Since in a group, every element has an unique inverse element, it follows that the solution is unique.

I don't know, it just looks too obvious, I may be missing something:

(also: I'm not a math major. I like doing proofs just for fun, and I don't really have that much of practice (yet), so forgive any lack of rigor or something like that. )

Is that it?

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