$1 =2?$

Algebra Level 2

Let's prove that $1 =2$ by using two variables, $a$ and $b$. Before we start, let's let $a=b$. Now, we can prove that $1=2$. $1) \ a = b \ || \ \text{Given}$

$2) \ a^2=ab \ || \ \text{Multiply both sides by} \ a$

$3) \ a^2-b^2=ab-b^2 \ || \ \text{Subtract both sides by} \ b^2$

$4) \ (a+b)(a-b)=b(a-b) \ || \ \text{Factor both sides}$

$5) \ (a+b)=b \ || \ \text{Divide both sides by} \ (a-b)$

$6) \ a + a = a \ || \ \text{Substitute} \ a \ \text{for} \ b$

$7) \ 2a = a \ || \ \text{Addition}$

$8) \ 2 = 1 \ || \ \text{Divide both sides by} \ a$

Which step is incorrect?

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