- #1

- 43

- 0

## Homework Statement

Determine whether the operation has an identity element.

x*y = 3xy

## Homework Equations

e*x = x*e = x, if this holds, e is an identity element

## The Attempt at a Solution

My attempt:

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!