Let * be binary operation defined on R by a * b = 1 + ab, ∀ a, b ∈ R. Then the operation * is ______.

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Let * be binary operation defined on R by a * b = 1 + ab, ∀ a, b ∈ R. Then the operation * is commutative but not associative. Explanation: Given that * is a binary operation defined on R by a * b = 1 + ab, ∀ a, b ∈ R So, we have a * b = ab + 1 = b * a So, * is a commutative binary operation. Now, a * (b * c) = a * (1 + bc) = 1 + a(1 + bc) = 1 + a + abc Also, (a * b) * c = (1 + ab) * c = 1 + (1 + ab)c = 1 + c + abc Thus, a * (b * c) $\neq$ (a * b) * c Hence, * is not associative. Therefore, * is commutative but not associative.

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