I'm stuck on this particular concept...
Soooo when is it that i.e. but probably if exists then we can multiply to the right by so we get . But how can we know before hand?
If you know that , then is invertible, which would imply that That's one condition that is sufficient. It's not necessary. As a counterexample, just let , and
Note: you're actually going to want to multiply on the left by , if it exists, in order to eliminate the 's.