Ok, so I like math. I found this simple proof when I was in college and thought it was nifty. But, there is an error in it that nullifies it's argument. Can you find it?

a = b

a^2 = a*b

a^2 - b^2 = a*b - b^2

(a + b)*(a - b) = b*(a - b)

(a + b) = b

b + b = b

2b = b

2 = 1

If you have any other fun math problems or proofs list them! I realize that this probably isn't going to be a popular subject, but as a math geek I was hoping that perhaps others might think it is interesting.