giả sử\(\left|x.y\right|=\left|x\right|.\left|y\right|\)
\(\Leftrightarrow\left|x.y\right|:\left|x\right|=y\)
\(\Rightarrow\left|x\right|=\left|y\right|\)
\(\Rightarrow\left|xy\right|=\left|x\right|.\left|y\right|\)
suy ra điều phải chứng minh
\(\left|x.y\right|=\left|x\right|.\left|y\right|\)
\(\Leftrightarrow\left|x.y\right|:\left|x\right|=\left|y\right|\)
\(\Leftrightarrow\left|y\right|=\left|y\right|\)
Vậy \(\left|x.y\right|=\left|x\right|.\left|y\right|\)