# Positive Definite Matrix Question

I am having some little difficulties to show the following:

Let $M$ be a symmetric positive square matrix. I must show that $I-M$ is positive definite matrix if and only if $M^{-1}-I$ is positive definite.

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You can assume that $M$ is diagonal. Can you solve it then? –  user27126 Jan 13 '13 at 5:58

thanks a lot. I never noticed that $eig(I-M)=eig(I)-eig(M)$ –  ChuckM Jan 13 '13 at 6:18