Prove that for all a,b in a ring R,
The hint says use:
Since any integer has a negative, we know
Multiple by b:
How can I show from the above?
Interesting approach (I don't have a problem with it). Note that . So the first part follows right away: .
For the second part, you do pretty much the same thing; however, you start with and then multiply by on the left:
Then because '=' is transitive, it now follows that .
I hope this makes sense.