is there an algebraic way to show this? I mean i understand why it's true but other than just saying it in a sentence is there something more fancy?
and also, does this hold true for (AB)^t = e, where A^t=e and B^t=e for some positive integer t.?
The effect of
would be moving it to
. So ...
Ah, fantastic, a much better way to see things.
Also, to clarify my statement, I meant that assuming you were doing that for all t>0 integers, it will happen to be true for some of them that it's true and that won't imply that both are the identity.