kengr

I know it's wrong, but I can't spot the error.

Oh, wait.

They can't substitute in "a" for "b" in the third line from the bottom. You're solving for A. You can't do that if you monkey around with the variables. This is how it's supposed to fall out:

Given that A = B,

A² = AB

A² - B² = AB - B²

(A + B)(A - B) = B(A-B)

A + B = B

A = 0

Then solve for B:

A = B
A = 0

Therefore, B = 0.

This is why you don't monkey around with the variables.