Question

a binary operation defined on R, by a*b=2a/(a-b) , a≠b,a,b∈R. Then the value of b*a when a*b=4 is

Answer 1

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Correct option is

B

Commutative but not Associative

A binary operation ∗ on A is associative if  ∀a,b,c∈A, 

(a∗b)∗c=a∗(b∗c) and 

A binary operation ∗ on A is commutative if  ∀a,b∈A, 

a∗b=b∗a

a∗b=4a+b is commutative as:

a∗b=b∗a⇒4a+b=4b+a⇒4a+b=4a+b

which is true.

a∗b=4a+b is not associative as:

(a∗b)∗c=a∗(b∗c)⇒(4a+b)∗c=a∗(4b+c)⇒44a+b+c=4a+4b+c⇒16a+b+4c

Step-by-step explanation:

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