An operation * is defined on the set of real numbers by a*b = a + b + 1. If the identity elements is -1, find the inverse of the element 2 under *.

First, let's find the inverse of the element 2 under the operation * on the set of real numbers. The inverse of an element "a" under the operation "*" is another element "b" such that a*b = b*a = identity element. The identity element under the operation "*" is given as -1, so we have: 2 * b = b * 2 = -1 Substituting the value of the identity element, we get: 2 * b = b * 2 + 1 = -1 Simplifying the equation, we get: 2b = -3 b = -3/2 Therefore, the inverse of the element 2 under the operation * is -3/2. To check if this is correct, we can substitute the values of 2 and -3/2 into the operation * and see if we get the identity element: 2 * (-3/2) = -3/2 * 2 = -1 Since we get the identity element, we can confirm that the inverse of the element 2 under the operation * is -3/2. So, the answer to the question is option (C) -2.