Let (*) be a binary operation on a natural number defined by a * b = a - b + (ab)\(^2\), then find 3 * 5

Let '*' and '^' be two binary operations such that a * b = a\(^2\)b and a ^ b = 2a + b. Find (-4 * 2) ^ (7 * -1).

Let a binary operation '*' be defined on a set A. The operation will be commutative if

If p * q = 2p + pq + q, find p  when ( p * 2) - (p * 1) = 40

A binary operation * is defined on a set of real numbers by x*y = x\(^y\) for all values of x and y, if x * 2 = x, find the possible values of x.