Question

Help please!

Let A be an n×n matrix, whose entries could be real or complex numbers. Suppose
that the diagonal entries of A are much larger than the size of the other entries in the
same row, in the sense that for each row i

2||aii|| > ||ai1|| + ||ai2|| + ||ai3|| + · · · + ||ain||.
Prove that A is invertible. (Hint: How is A not being invertible connected to the
eigenvalues of A?)