July 12th, 2017, 04:58 AM  #1 
Newbie Joined: Jul 2017 From: KOLKATA Posts: 12 Thanks: 1  Relations and Functions
Let * be a binary operation on the set Q of rational numbers as follows such that 1) a * b = a^2 + b^2 2) a * b = a(b^2) Does any of the above operations have an identity element? If not, why? Last edited by skipjack; July 12th, 2017 at 07:44 AM. 
July 12th, 2017, 07:16 AM  #2 
Member Joined: Oct 2009 Posts: 97 Thanks: 33 
Did you try anything? Why don't you start trying some obvious constants first to see whether they work? If they don't, then write down the equation for what it means to be a neutral element and try to solve it. Last edited by skipjack; July 12th, 2017 at 07:42 AM. 
July 12th, 2017, 09:34 AM  #3 
Newbie Joined: Jul 2017 From: KOLKATA Posts: 12 Thanks: 1 
Have posted it for solution . Not for advises

July 12th, 2017, 10:12 AM  #4 
Member Joined: Oct 2009 Posts: 97 Thanks: 33 
How will you learn anything if we just solve it for you?

July 12th, 2017, 10:18 AM  #5 
Newbie Joined: Jul 2017 From: KOLKATA Posts: 12 Thanks: 1 
If you have the solution post it . Otherwise , please refrain from merely advising which does not serve any purpose

July 12th, 2017, 10:31 AM  #6 
Newbie Joined: May 2017 From: California Posts: 11 Thanks: 1 
r u the same micromass from pf?

July 12th, 2017, 10:34 AM  #7 
Member Joined: Oct 2009 Posts: 97 Thanks: 33 
Yep, I am

July 12th, 2017, 10:35 AM  #8 
Member Joined: Oct 2009 Posts: 97 Thanks: 33  
July 12th, 2017, 10:42 AM  #9 
Newbie Joined: Jul 2017 From: KOLKATA Posts: 12 Thanks: 1 
Only such advises of yours , as posted above , really serves no purpose . It seems you too , do not have the answer to the query

July 12th, 2017, 11:09 AM  #10 
Global Moderator Joined: Dec 2006 Posts: 17,533 Thanks: 1322 
1) If b is an identity, a = a * b = aÂ² + bÂ² for any value of a, which clearly isn't the case. 2) If b = 1, a * 1 = a(1) = a for any value of a, so 1 is a right identity. 

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