Answer :

Given that,

‘*’ be binary operation defined on R by a * b = 1 + ab, a, b R

A binary operation ‘*’ is commutative if a*b = b*a a, b R


a*b = 1+ab = 1+ba [ ab=ba since multiplication is commutative

on R]

1+ba = b*a

a*b = b*a a, b R

So, ‘*’ is commutative on R.

A binary operation ‘*’ is associative if (a*b)*c = a*(b*c) a, b,c R


(a*b)*c = (1+ab)*c = 1+(1+ab)c = 1+c+abc

a*(b*c) = a*(1+bc) = 1+a(1+bc) = 1+a+abc

(a*b)*c ≠ a*(b*c)

So, ‘*’ is not associative on R.

Hence, ‘*’ is commutative but not associative on R.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses

| Let * be a binaMathematics - Board Papers

Find the idMathematics - Board Papers

Let f : A Mathematics - Exemplar

Show that the binMathematics - Board Papers

Determine whetherRD Sharma - Volume 1

Fill in theMathematics - Exemplar