Pure math, 2 = 1!

Algebra Level 1

Consider the following equation (proved).

\[a = b \\ a \times a = b \times a \\ a^{2} = ab \\ a^{2} - b^{2} = ab - b^{2} \\ (a + b)(a - b) = b(a - b) \\ a + b = b \\ b + b = b \\ 2b = b \\ 2 = 1\]

Is the proof correct?

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