About Factors of numbers

Question:
Suppose that a and b are integers and that a|b and b|a.
Prove that a=b or a=-b.

My answer to the question:
Since a|b there is an integer z such that b=a*z
Since b|a there is an integer w such that a=b*w
Substitute b=a*z to a=b*w,
a=a*z*w
a/a=z*w
z*w=1

Multiply b=a*z and a=b*w,
a*b=a*z*b*w
a*b=a*b*(z*w)
a*b=a*b*1
a*b=a*b

Then I am stuck from here, I cannot figure out how to prove a=b and a=-b from this point. Can you help me please?