# How do I find idempotent elements of binary operation?

• Apr 21st 2012, 10:14 AM
zzizi
How do I find idempotent elements of binary operation?
Hi, can anyone out there help with this? (Worried)

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.

• Apr 21st 2012, 10:26 AM
a tutor
Re: How do I find idempotent elements of binary operation?
Do you require (a,b)*(a,b)=(a,b)?

What is (a,b)*(a,b)?
• Apr 21st 2012, 10:41 AM
zzizi
Re: How do I find idempotent elements of binary operation?
I was hoping someone could explain this to me. Btw I made a mistake it should have been a minus sign.
• Apr 21st 2012, 10:46 AM
a tutor
Re: How do I find idempotent elements of binary operation?
Do you mean (a,b)*(c,d) = (ad-bc,bd)?
• Apr 21st 2012, 10:54 AM
zzizi
Re: How do I find idempotent elements of binary operation?
Yes
• Apr 21st 2012, 12:06 PM
a tutor
Re: How do I find idempotent elements of binary operation?
(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).
• Apr 21st 2012, 12:30 PM
zzizi
Re: How do I find idempotent elements of binary operation?
Thank you so much (Yes)

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