Could you give me please some tips or direction on how should I deal with the following problem? 

$A = \left( a\_{i,j} \right)$ is a Matrix from $M(n\times n, \mathbb{R})$ so that for all $ i\in \left \{ 1,\ldots,n \right \}$ exists $j$ such that:

$$\left|a\_{i,j}\right|>\left|a\_{i,1}\right|+\left|a\_{i,2}\right|+\ldots+\left| a\_{i,i-1}\right|+\left|a\_{i,i+1}\right|+ \cdots +\left | a\_{i,n} \right|.$$

I have to prove, that $\operatorname{rank}\left ( A \right ) = n$.

Thank you in advance.