# Homework Help: Linear Algebra - Diagonalization question

1. Dec 7, 2011

### starcoast

1. The problem statement, all variables and given/known data
Suppose A = SΛS$^{-1}$. What is the eigenvalue matrix for A + 2I? What is the eigenvector matrix? Check that A + 2I = ()()()$^{-1}$.

3. The attempt at a solution
I think I'm pretty close I'm just not sure what to do next:
A + 2I = SΛS$^{-1}$ + 2I
= SΛS$^{-1}$ + 2SS$^{-1}$

??? now what?

2. Dec 8, 2011

### I like Serena

Use the distributive property of matrix multiplication?