Thread: How do I find idempotent elements of binary operation?

Hi, can anyone out there help with this?

If Z x Z = {(a,b): a,b are integers} and if the binary operation on Z x Z by (a,b)*(c,d) = (ad,-bc),bd

How do I show that the operation * has idempotent elements.

I would really appreciate a step by step explanation.

Many thanks in advance!

Do you require (a,b)*(a,b)=(a,b)?

What is (a,b)*(a,b)?

I was hoping someone could explain this to me. Btw I made a mistake it should have been a minus sign.

Do you mean (a,b)*(c,d) = (ad-bc,bd)?

Yes

(a,b)*(a,b)=(ab-ab,b^2)=(0,b^2). If (a,b)*(a,b)=(a,b) then a=0 and b=b^2. So you have (0,1) or (0,0).

Thank you so much

If you or anyone else can point me to a tutorial site that can explain a bit more about finding idempotent elements of binary operations, it would be appreciated.

Thanks