Mathematical fallacy (inspired)

Number Theory Level 2

In the following 6 lines, it is given that \(a=b\):

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