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
A
p
B
p -1
C
p/(p-1)
D
p/(p+1)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
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\(^{-1}\) =\(\frac{-P}{(P-1)}\)
= \(\frac{P}{(P-1)}\)
Source: Myschool Past Questions Archive (Record #719)