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Question
Let * be the binary operation defined on Q. Find which of the following binary operations are commutative
a * b = (a – b)2 ∀ a, b ∈ Q
Solution
Given that * is a binary operation defined on Q.
a * b = (a – b)2, ∀ a, b ∈Q
b * a = (b –a)2
Since, (a – b)2 = (b – a)2
Thus, * is commutative.
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