(adsbygoogle = window.adsbygoogle || []).push({}); a = b

multiply by a
a^2 = ab

subtract b^2
a^2 - b^2 = ab - b^2

factor
(a-b)(a+b) = b(a-b)

divide
a + b = b

a=b, so substitute b for a
b + b = b

combine
2b = b

divide
2 = 1

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Your argument is invalid due to self containing fallacies relating to the notion of 0.