$A = \begin{pmatrix} 0 & 1 &1 \\ 1 & 0 &1 \\ 1& 1 &0 \end{pmatrix} $
The matrix $(A+I)$ has rank $1$ , so $-1$ is an eigenvalue with an algebraic multiplicity of at least $2$ .
I was reviewing my notes and I don't understand how the first statement implies the second one.
Can anyone please explain how rank 1 of $(A + I)$ implies $-1$ is an eigenvalue with an algebraic multiplicity of $2$?
Thank you in advance.