1=2?

Algebra Level 2

Let there be 2 variables a and b where, a=b 1. multiply a on both the sides, a^{2}=ab 2. subtract b^2 on both the sides, a^{2}-b^{2}=ab-b^{2} 3. since a^{2}-b^{2}=(a+b)(a-b), (a+b)(a-b)=b(a-b) [taking b common] 4. dividing by (a-b) on both the sides, we get, a+b=b 5. but a=b as given in the first step, b+b=b 2b=b 6. dividing by b on both sides, 2=1 Which step did I make a mistake?

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