Proof that 2=1

1) $a = b$ . Given. 2) $a^2 = ab$ . Multiply both sides by a. 3) $a^2-b^2 = ab-b^2$ . Subtract $b^2$ from both sides. 4) $(a+b)(a-b) = b(a-b)$ . Factor both sides. 5) $(a+b) = b$ . Divide both sides by $(a-b)$ 6) $a+a = a$ . Substitute $a$ for $b$ . 7) $2a = a$ . Addition. 8) $2 = 1$ . Divide both sides by $a$ .