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Question
If the binary operation o is defined by aob = a + b − ab on the set Q − {−1} of all rational numbers other than 1, shown that o is commutative on Q − [1].
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Solution
\[\text{Let a}, b \in Q - \left\{ - 1 \right\} . \text{Then}, \]
\[a o b = a + b - ab\]
\[ = b + a - ba\]
\[ = b o a\]
\[\text{Therefore},\]
\[ a o b = b o a, \forall a, b \in Q - \left\{ - 1 \right\}\]
Thus, o is commutative on Q - {1}.
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