Does there exist a matrix A such that A+cI is invertible for all complex c?

[jayred]

Homework Statement

Does there exist a matrix A such that the entire family A + cI is invertible for all complex numbers c?

Homework Equations

A matrix is invertible if det(A) != 0


I really have no clue where to go with this problem. Any hints or suggestions would be greatly helpful, even if you can't give an answer to the problem.

 

[Billy Bob]

What kind of function is f(c)=det(A+cI)?