1 = 2 Proof Challenge

by Luke Van Horn ('19)
​

Here is a fun challenge that I found online. Obviously 1 does not equal 2. Try to find the problem with this proof!
Prove: 1=2
Given: a = b
a = b
a * a = b * a
a2 = ab
a2 - b2 = ab - b2
(a-b)(a+b) = b(a-b)
a+b = b
b+b = b
2b = b
2 = 1