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2=1? - math puzzle of the day

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Suppose: a = b

It then follows that
a * a = a * b
a^2 = a * b
a^2 - b^2 = a * b - b^2
(a - b) * (a + b) = (a - b) * b
a + b = b
a + a = a
2 * a = 1 * a
2 = 1

Is this derivation really correct? Or is there somewhere a mistake? If so, where?

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