Linear mapping/0/Exercise/Solution

Due to the additivity of a linear mapping, we have

${}\varphi (0)=\varphi (0+0)=\varphi (0)+\varphi (0)\,.$

Addition with the negative element of ${}\varphi (0)$ that is, with ${}-\varphi (0)$, yields

${}0=\varphi (0)\,.$

To the exercise