Chapter 6, Problem 2CTB

Let A be a $4\times 4$ matrix with real entries that has all 1's on the main diagonal (i.e., $a_{11}=a_{22}=a_{33}=a_{44}=1$ ). If A is singular and ${\lambda }_1=3+2i$ eigenvalue of A, then what, if anything, is it possible to conclude about the values of the remaining eigenvalues ${\lambda }_2,{\lambda }_3,$ and ${\lambda }_4?$ Explain.