I get stuck in the following question:

Why does a locally symmetric space of compact type $M$ split locally irreducible components of dimension $\geq 2$ which are Einstein? In particular, why are all eigenvalues of Ricci curvature ${\rm Ricci}(M)$ strictly positive and why does each eigenvalue have a multiplicity of at least 2?

I don't know if the question is too easy on MO. Could you please give me some help with the details? Thanks in advance. By the way, are there some nice references for these questions to refer to?