# Prove that A is invertible [duplicate]

$$A \text{ is a Matrix in } \mathbb{R}^{n\times n} \text{ such that:} \left | a_{i,i} \right | > \sum_{\substack {j=1 \\j\neq i}}^{n} \left | a_{i,j} \right | \quad \text{ for all } i \in \left \{ {1..n} \right \}$$ Prove that A is invertible.