Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
0 votes

Find if the given operation has identity: $\;\; a \ast b = a^2 + b^2$

This question has multiple parts. Therefore each part has been answered as a separate question on Clay6.com

Can you answer this question?

2 Answers

0 votes
  • An element $e \in N $ is an identify element for operation * if $a \ast e=e \ast a$ for all $a \in N$
Given $ a *b =a^2+b^2$
Let e be an identity element of * operation
By definition of identity element we have a*e=e*a = a
but by definition of * operation $ a *e =a^2+e^2$ =>$ a=a^2+e^2$ =>$ e^2= a-a^2$
=> e = square root of$ a=a^2$, but square root of $a=a^2$ does not always belong to N for all a in N
Therefore the operation * defined by $ a *b =a^2+b^2$ has no identity.
answered Mar 20, 2013 by thagee.vedartham
0 votes
Operation has no identity
answered Mar 30 by balaji.thirumalai

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App