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
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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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