Find the error in the following proof that $2 = 1.$Consider the equation $a = b.$ Multiply both sides by a to obtain $a^{2} = ab.$ Subtract $b^{2}$ from both sides to get $a^{2}-b^{2}=ab-b^{2}.$ Now factor each side $, (a+b)(a−b) = b(a−b),$ and divide each side by $(a−b)$ to get $a+b = b.$ Finally, let $a$ and $b$ equal $1,$ which shows that $2 = 1.$
