Which one of the following relations on Z is equivalence relation?

A relation is equivalent if it is symmetric, transitive and reflexive.
$xR,y\iff \left|x\right|=\left|y\right|$
checking for reflexive
$x{R}_{1}x;\left|x\right|=\left|x\right|$  satisfies $R_1,R_1$  is reflexive  
$x{R}_{1}y\Rightarrow \left|x\right|=\left|y\right|$, $y{R}_{1}x\Rightarrow \left|y\right|=\left|x\right|$  as equality communicative ,$R_1$ is symmetric
Checking for transitive.
Let $(x,y)$ and $(y,z)$ satisfy $R_1$
$\Rightarrow x{R}_{1}y\iff \left|x\right|=\left|y\right|$
$y{R}_{1}z\iff \left|y\right|=\left|z\right|$
$\therefore x{R}_{1}z\iff \left|x\right|=\left|z\right|$
$\therefore \left(x,z\right)$ satisfies $R_1$
$\therefore R_1$ is equivalent