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(D) On $Q$,the operation $^*$ is defined as $a * b = a + ab$.To check for commutativity:$1 * 2 = 1 + (1 	imes 2) = 1 + 2 = 3$$2 * 1 = 2 + (2 	imes 1

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Neither Commutative nor Associative

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(D) On $Q$,the operation $^*$ is defined as $a * b = a + ab$.To check for commutativity:$1 * 2 = 1 + (1 	imes 2) = 1 + 2 = 3$$2 * 1 = 2 + (2 	imes 1) = 2 + 2 = 4$Since $1 * 2 
eq 2 * 1$,the operation $^*$ is not commutative.To check for associativity:$(1 * 2) * 3 = (1 + 1 	imes 2) * 3 = 3 * 3 = 3 + (3 	imes 3) = 3 + 9 = 12$$1 * (2 * 3) = 1 * (2 + 2 	imes 3) = 1 * 8 = 1 + (1 	imes 8) = 1 + 8 = 9$Since $(1 * 2) * 3 
eq 1 * (2 * 3)$,the operation $^*$ is not associative.Thus,the operation $^*$ is neither commutative nor associative.

Let $^$ be a binary operation on the set $Q$ of rational numbers defined as $a b = a + ab$. Is the operation $^*$ commutative and associative?

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Let $^*$ be a binary operation on the set $Q$ of rational numbers defined as $a * b = a + ab$. Is the operation $^*$ commutative and associative?