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(A) The binary operation is defined as $a * b = a^{2} + b^{2}$.To check for commutativity,we need to verify if $a * b = b * a$ for all $a, b \in Q$.Gi

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(A) The binary operation is defined as $a * b = a^{2} + b^{2}$.To check for commutativity,we need to verify if $a * b = b * a$ for all $a, b \in Q$.Given $a * b = a^{2} + b^{2}$.Since addition is commutative in the set of rational numbers,we have $a^{2} + b^{2} = b^{2} + a^{2}$.By the definition of the operation,$b^{2} + a^{2} = b * a$.Therefore,$a * b = b * a$ for all $a, b \in Q$.Thus,the binary operation $*$ is commutative.

Let $$ be a binary operation defined on the set of rational numbers $Q$. Determine whether the binary operation defined by $a b = a^{2} + b^{2}$ 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 $a * b = a^{2} + b^{2}$ for all $a, b \in Q$ is commutative.