Math Help - groups

1. groups

How to prove that in a group, the equations ax=b and ya=b are solvable for any a,b in G.
Conversely how to show that any semigroup having this property contains a unit and is a group.

2. Thanks a lot!
Can you help me on the first part:
How to prove that in a group, the equations ax=b and ya=b are solvable for any a,b in G.
Thanks again!

3. Originally Posted by thomas_donald
Thanks a lot!
Can you help me on the first part:
How to prove that in a group, the equations ax=b and ya=b are solvable for any a,b in G.
Thanks again!
That is because $ax=b\Leftrightarrow x=a^{-1}b,ya=b\Leftrightarrow y=ba^{-1}$

4. Thanks

Thank you very much for your help.