Find the inverse of \(P\) under the binary operation * if \(p^{*} q=p+q-p q\) wherd ind \(q\) are real number and zero is the identity
A. \(p\) B. \(p-1\) C. \(P_{p+1}\) D. \(p_{p-1}^{p-1}\)
Correct Answer: D
Explanation
Let the inverse of \(p\) he \(P^{-1}\) Thên \(p^{*} p^{-1}\) e where 'e ' is the identify elemant Now \(p^{*} p^{-1}=e\) \(\Rightarrow p+p^{-1}-p p^{-1}=0\) (definition of * and identity element benig 0 ) \(P+p^{-1}-(1-p)-0\) \(p^{-1}(1-p)=-p\) \(p^{-1}={ }^{p} / p-1\) by dividing foth sigde by 1-p hence the invesse of \(p=\)P/P-1
