Determine if the following problem is symmetric and transitive

[Meager]

Homework Statement

Suppose ~ is defined on the whole numbers by a~b iff ab² is a perfect cube. Determine if ~ is
symmetric
transitive

Homework Equations

ab² must ba²

The Attempt at a Solution

I tried using different numbers, but it isn't coming out as a perfect square.

For example, I said a=1
b=0........ Then this works.
Using other numbers it fails.

Should a=b?

 

[tiny-tim]

Welcome to PF!

Hi Meager! Welcome to PF!

Suppose ~ is defined on the whole numbers by a~b iff ab² is a perfect cube. Determine if ~ is
symmetric
transitive

Hint: write a and b as a product of their prime factors.