Absorbing Markov chain arithmetic multiplicity of eigenvalue 1

Question

Im trying to demostrate that:

Theorem In an Absorbent Markov chain, the eigenvalue $\lambda = 1$ has a arithmetic multiplicity equal to the number of absorbent states (columns such that $m_{ii} = 1$) and all the others eigenvalues are $| \lambda | < 1$.

But all my tries were futile.