\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
The following "proof" by equivalence leads to the absurd conclusion that \(2=1\). Identify the incorrect step and explain the error in the reasoning.$$\begin{aligned} && a &= b \\ \Leftrightarrow && a^2 &= ab \\ \Leftrightarrow && a^2 - b^2 &= ab - b^2 \\ \Leftrightarrow && (a-b)(a+b) &= b(a-b) \\ \Leftrightarrow && a+b &= b \\ \Leftrightarrow && 2a &= a \\ \Leftrightarrow && 2 &= 1\end{aligned}$$
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