Let ∗ be a binary operation on the set Q of rational numbers as follows:
a ∗ b = (a – b)²
Find which of the binary operations are commutative and which are associative.
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Step-by-step explanation:
1) Associative : (a\ast b)\ast c=ab^{2}+c=ab^{2}+c^{2}$$
a∗(b∗c)=a+(bc
2
)
=(a∗b)∗c
Not Associative.
(2) Commative : a∗b=ab
2
b∗a=ba
2
=a∗b
Not Commutative.
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