Linear Algebra - Diagonalization question

[starcoast]

Homework Statement

Suppose A = SΛS^{-1}. What is the eigenvalue matrix for A + 2I? What is the eigenvector matrix? Check that A + 2I = ()()()^{-1}.

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?

 

[I like Serena]

Use the distributive property of matrix multiplication?