Finding eigenvalues using trace.

Question

Matrix A is

$$A = \pmatrix {1&1&1\\ 3&3&4 \\ 5&5&4}$$

Within the parentheses is each column. It is given that one eigenvalue is -1. It says to use the trace. I know how to set it up but I'm confused because there are two eigenvalues I need to find.

Answer 1

Hint:

This matrix has rank $2$, hence its kernel is non-trivial.