# Eigen Vectors Concept: Proving

A matrix G has eigen vector e How can i prove that e is also an eigen vector for G+k I where I is an identity matrix. (they are all 3x3). I tried using Ae = k e i didnt work

$$(\mathbf{G}+k\mathbf{I})v=\lambda v+k v=(\lambda+k)v$$
Which means $v$ is an eigenvector of $\mathbf{G}+k\mathbf{I}$ associated to the eigenvalue $\lambda+k$