# Let $\left| {{a_{ii}}} \right| > \sum\limits_{i \ne j} {\left| {{a_{ij}}} \right|}$.Why does $A$ is nonsingular? . [duplicate]

Let $A \in {M_n}$ and $\left| {{a_{ii}}} \right| > \sum\limits_{j \ne i} {\left| {{a_{ij}}} \right|}$.Why does $A$ is nonsingular?
• You should write $j \ne i$, not $i \ne j$, since you're summing over $j$. – Keith Jun 2 '15 at 3:59
Hint. Let $X = (x_j)$ be a nonzero column matrix. Prove that $AX \ne 0$ by considering the index $s$ for which $x_s$ has the largest absolute value.