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July 12th, 2017, 05:58 AM   #1
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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?
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Last edited by skipjack; July 12th, 2017 at 08:44 AM.
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July 12th, 2017, 08:16 AM   #2
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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.
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Last edited by skipjack; July 12th, 2017 at 08:42 AM.
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July 12th, 2017, 10:34 AM   #3
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Have posted it for solution . Not for advises
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July 12th, 2017, 11:12 AM   #4
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How will you learn anything if we just solve it for you?
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July 12th, 2017, 11:18 AM   #5
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If you have the solution post it . Otherwise , please refrain from merely advising which does not serve any purpose
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July 12th, 2017, 11:31 AM   #6
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r u the same micromass from pf?
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July 12th, 2017, 11:34 AM   #7
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Yep, I am
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July 12th, 2017, 11:35 AM   #8
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Quote:
Originally Posted by arybhatta01 View Post
If you have the solution post it . Otherwise , please refrain from merely advising which does not serve any purpose
Helping you to get the solution doesn't serve any purpose?
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July 12th, 2017, 11:42 AM   #9
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Only such advises of yours , as posted above , really serves no purpose . It seems you too , do not have the answer to the query
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July 12th, 2017, 12:09 PM   #10
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1) If b is an identity, a = a * b = a² + b² 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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