# Eigenvalues of Matrix with 1s everywhere but diagonal [duplicate]

I'm not sure if this type of matrix has a name, but I feel as if there's a trick to finding the eigenvalues that i'm missing:

$$a \in R$$ $$M = \begin{bmatrix} 1 + a & 1 & 1 \\[0.3em] 1 & 1 + a & 1 \\[0.3em] 1 & 1 & 1+ a \end{bmatrix}$$

## marked as duplicate by Davide Giraudo, Hakim, Etienne, vonbrand, Asaf Karagila♦May 23 '14 at 18:38

Do you know the eigenvalues in the case $a = 0$?
Do you know the eigenvalues of $A + a \, I$, where $I$ is the identity in terms of the eigenvalues of $A$?
The eigenvalues of $M$ are $a+3, \ a, \ a$.