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Algebra Level 2

Which solution to the equation \(x^2 = x\) contains an error?

\(\begin{align*} \text{Original: }\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; x^2 &= x\\ \text{Divide both sides by x:}\;\;\;\;\; x &= 1 \end{align*}\)

\(\begin{align*} \text{Original: }\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; x^2 &= x\\ \text{Subtract x from both sides:}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;x^2 - x &= 0\\ \text{Factor:}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; x(x-1) &= 0\\ \text{Use the Zero Product Property:}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; x =0&, x = 1 \end{align*}\)

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