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Let * be a binary operation on the set Q of all rational numbers given as a * b = (2a – b)2 for all a, b ∈ Q. Find 3 * 5 and 5 * 3. Is 3 * 5 = 5 * 3?

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It is given that a * b = (2a – b)2

We know that

3 * 5 = (2 × 3 – 5)2 = 1

5 * 3 = (2 × 5 – 3)2 = 49

Therefore, 3 * 5 ≠ 5 * 3

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