\(2ab=a+b\)
\(a-2ab+b=0\)
\(2a-2.2ab+2b=0\)
\(2a-2b\left(2a-1\right)=0\)
\(2a-1-2b\left(2a-1\right)=-1\)
\(\left(2a-1\right)\left(1-2b\right)=-1\)
\(\Rightarrow2a-1=1\) thì \(1-2b=-1\) \(\Rightarrow a=1\) thì \(b=1\)
\(\Rightarrow2a-1=-1\) thì \(1-2b=1\) \(\Rightarrow a=0\) thì \(b=0\)
Vậy \(\left(a;b\right)=\left(0;0\right)\left(1;1\right)\)