Let 'o ' be a binary operation on the set Q_0 of all non-zero rational numbers defined by a ^* b= ab 2 for all a,b _0. Find the invertible elements of Q_0.

We have, a ^* b= ab 2 for all a,b _0 Let b _0 be the inverse of a _0 with respect to ^*, then, a ^* b = b ^* a = e for all a _0 ab 2 =e ab 2 =2 =4 a Thus, b=4 a is the inverse of a with respect to ^*.

Let 'o ' be a binary operation on the set Q_0 of all non-zero rat…

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