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An operation * is defined on the set, R, of real numbers by \(p * q = p + q + 2pq\). If ...

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

A. \(\frac{-1}{2}\)
B. \(0\)
C. \(\frac{2}{3}\)
D. \(2\)




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