Problem 3. Let * be a binary operation on the set of real numbers R defined as follows: a * b = a + b – 3(ab)², where a,b e R Prove that * is commutative but not associative algebraic operation on R. Solution. Find the identity element for * . Solution. Show that 1 has two inverses with respect to *. Solution.

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ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
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Problem 3. Let * be a binary operation on the set of real numbers R defined as follows:
a * b = a + b – 3(ab)², where a,b e R
Prove that * is commutative but not associative algebraic operation on R.
Solution.
Find the identity element for * .
Solution.
Show that 1 has two inverses with respect to *.
Solution.
Transcribed Image Text:Problem 3. Let * be a binary operation on the set of real numbers R defined as follows: a * b = a + b – 3(ab)², where a,b e R Prove that * is commutative but not associative algebraic operation on R. Solution. Find the identity element for * . Solution. Show that 1 has two inverses with respect to *. Solution.
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