$\begin{array}{l}
A = \left\{ {x \in Z|\left| {{x^2} - 4x + 3} \right| + \left| {2x - 2} \right| = 0} \right\}\\
\Rightarrow \left| {{x^2} - 4x + 3} \right| + \left| {2x - 2} \right| = 0\\
\Leftrightarrow \left| {\left( {x - 1} \right)\left( {x - 3} \right)} \right| + \left| {2\left( {x - 1} \right)} \right| = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x = 1\\
x = 3
\end{array} \right.\\
\Rightarrow A = \left\{ {1;3} \right\}
\end{array}$
