Let's solve this problem step by step. We are given the binary operation * defined by p*q = p + q - pq, where p and q are real numbers and zero is the identity. We need to find the inverse of p under this operation.

The inverse of an element p under a binary operation * is an element q such that p*q = q*p = e, where e is the identity element.

In this case, the identity element is zero, so we need to find an element q such that p*q = 0.

Substituting the definition of the binary operation into this equation, we get: p + q - pq = 0. Solving for q, we find that q = p/(p-1).

Therefore, the inverse of p under the binary operation * defined by p*q = p + q - pq is p/(p-1).