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An operation * is defined on the set, R, of real numbers by ...

An operation * is defined on the set, R, of real numbers by pq=p+q+2pq. If the identity element is 0, find the value of p for which the operation has no inverse.

A.

12

B.

0

C.

23

D.

2

Correct answer is A

Given the formula for p * q as: p+q+2pq and its identity element is 0, such that if, say, t is the inverse of p, then

pt=0, then p+t+2pt=0

t = \frac{-1}{1 + 2p} is the formula for the inverse of p and is undefined on R when

1 + 2p) = 0 i.e when 2p = -1; p = \frac{-1}{2}.