Question

*:R×R gives R is given by a*b=3a^2-b. Find the value of 2*3.Is * commutative? Justify your answer.

Answer 1

Answer :

★ 2*3 = 9

★ * is not commutative

Solution :

Given Binary Operation :

* : R × R → R , a*b = 3a²b - b

★ Value of 2*3 :-

=> 2*3 = 3×2² - 3

=> 2*3 = 3×4 - 3

=> 2*3 = 12 - 3

=> 2*3 = 9

Hence , 2*3 = 9

★Whether * is commutative :-

Note : A binary Operation * is said to be commutative if a*b = b*a .

Now ,

=> LHS = a*b

=> LHS = 3a² - b

Also ,

=> RHL = b*a

=> RHS = 3b² - a

LHS ≠ RHS

Since , a*b ≠ b*a thus the given binary Operation * is not commutative .