Question

An operation* is defined by a set of x*y=x+y+3xy as an element of real numbers, find the identity element

Answer 1

If y is the identity element, then x*y = x
x+y+3xy = x
y+3xy = 0
y(3x+1) = 0
y=0
so 0 is the identity element

extra credit: what is the inverse of x?