Prove that $\|B\|_{\infty}<1$ with $B $ is defined by $$\begin{pmatrix} 0 & \frac{-a_{12}}{a_{11}} &\frac{-a_{13}}{a_{11}} & \frac{-a_{14}}{a_{11}} \\ \frac{-a_{21}}{a_{22}}&0 & \frac{-a_{23}}{a_{22}}& \frac{-a_{24}}{a_{22}}\\ \frac{-a_{31}}{a_{33}} & \frac{-a_{32}}{a_{33}} & 0 & \frac{-a_{34}}{a_{33}} \\ \frac{-a_{41}}{a_{44}}& \frac{-a_{42}}{a_{44}} & \frac{-a_{43}}{a_{44}} & 0 \\ \end{pmatrix}$$
Here $ \|B\|_{\infty}= \max_{1\le i \le 4}\left ( \sum_{j=1}^{n} |a_{ij}|\right )$
$\|B\|_{\infty}=\max\{\frac{a_{12}+a_{13}+a_{14}}{a_{11}},\frac{a_{21}+a_{23}+a_{24}}{a_{22}},\frac{a_{31}+a_{32}+a_{34}}{a_{33}},\frac{a_{41}+a_{42}+a_{43}}{a_{44}}\}$
But how to prove $\|B\|_{\infty}<1$ ?