JAMB - Mathematics (2000 - No. 12)
Find the inverse of p under the binary operation * defined by p*q = p + q - pq, where p and q are real numbers and zero is the identity
p
p -1
p/(p-1)
p/(p+1)
Maelezo
If P\(^{-1}\) is the inverse of P and O is the identity, Then P\(^{-1}\) * P = P * P\(^{-1}\) = 0
i.e. P\(^{-1}\) + P - P\(^{-1}\).P = 0
P\(^{-1}\) - P\(^{-1}\).P = -P
P\(^{-1}\)(1 - P) = -P
P\(^{-1}\) =\(\frac{-P}{(P-1)}\)
= \(\frac{P}{(P-1)}\)
i.e. P\(^{-1}\) + P - P\(^{-1}\).P = 0
P\(^{-1}\) - P\(^{-1}\).P = -P
P\(^{-1}\)(1 - P) = -P
P\(^{-1}\) =\(\frac{-P}{(P-1)}\)
= \(\frac{P}{(P-1)}\)