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)
Correct Answer: Option C
Explanation
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 = -P/(P-1)
= P/(P-1)