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

$Let a, b \in Q - \{- 1\} . Then, a o b = a + b - a b = b + a - b a = b o a Therefore, a o b = b o a, \forall a, b \in Q - \{- 1\}$

Thus, o is commutative on Q - {1}.

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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].

Let a, b∈Q--1. Then, a o b= a+b-ab =b+a-ba =b o aTherefore,a o b=b o a,∀ a, b∈Q--1 Thus, o is commutative on Q - {1}.

$Let a, b \in Q - \{- 1\} . Then, a o b = a + b - a b = b + a - b a = b o a Therefore, a o b = b o a, \forall a, b \in Q - \{- 1\}$

Thus, o is commutative on Q - {1}.