A student argues: 'Let $a = b$ . Then $a^{2} = ab$ , so $a^{2} - b^{2} = ab - b^{2}$ . Factorising, $(a + b) (a - b) = b (a - b)$ . Dividing by $(a - b)$ gives $a + b = b$ , so $2 b = b$ , hence $2 = 1$ .' Which step is invalid?

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