Determine whether the operation has an identity element.
x*y = 3xy
e*x = x*e = x, if this holds, e is an identity element
The Attempt at a Solution
x*z = z*x = 3xz, then 3xz = x <=> z = 1/3 => e = 1/3.
But the answer key in the back of the book says that this binary operation has no identity element. Am I wrong, or is the book? Thanks!