Question

A binary operation is defined on a set R, of really numbers a*b=a+b+2. Find the:
a) identity element under the operation *
b) inverse of b under the operation *?

Answer 1

If e is the identity, then
a*e = e*a = a
So, you need
a + e + 2 = a
Looks like e = -2
(Yes, -2 is really a number!)

The inverse of a means
a * a^{^-1} = the identity
So, what do you think?

Answer 2

a*a^-1