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(B) The binary operation is defined as $a * b = a + ab$.To check for commutativity,we compare $a * b$ with $b * a$.By definition,$a * b = a + ab$.Simi

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No,it is not commutative.

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(B) The binary operation is defined as $a * b = a + ab$.To check for commutativity,we compare $a * b$ with $b * a$.By definition,$a * b = a + ab$.Similarly,$b * a = b + ba = b + ab$.For the operation to be commutative,we must have $a * b = b * a$ for all $a, b \in Q$.This implies $a + ab = b + ab$.Subtracting $ab$ from both sides,we get $a = b$.Since $a = b$ is not true for all $a, b \in Q$,the operation is not commutative.Example: Let $a = 3$ and $b = 2$.$a * b = 3 * 2 = 3 + 3(2) = 3 + 6 = 9$.$b * a = 2 * 3 = 2 + 2(3) = 2 + 6 = 8$.Since $9 
eq 8$,$a * b 
eq b * a$.

Let $$ be a binary operation defined on the set of rational numbers $Q$. Determine whether the binary operation defined by $a b = a + ab$ for all $a, b \in Q$ is commutative.

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Let $*$ be a binary operation defined on the set of rational numbers $Q$. Determine whether the binary operation defined by $a * b = a + ab$ for all $a, b \in Q$ is commutative.

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For each binary operation $^*$ defined below,determine whether $^*$ is commutative or associative. On $Z$,define $a ^* b = a - b$.

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