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].

Answer 1

\[\text{Let a}, b \in Q - \left\{ - 1 \right\} . \text{Then}, \]

\[a o b = a + b - ab\]

\[ = b + a - ba\]

\[ = b o a\]

\[\text{Therefore},\]

\[ a  o  b = b o a, \forall a, b \in Q - \left\{ - 1 \right\}\]

Thus, o is commutative on Q - {1}.