Im currently reading "Linear Algebra, Fourth Edition,Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence"
At page 485 a theorem is located as follows:
Theorem 7.1 Let T be a linear operator on a vector space V, and let $\lambda$ be an eigen value of T. Then a)...
b)For any scalar $\mu\not=\lambda$, the restriction of $T-\mu I$ to $K_\lambda$ is injective.
Question: How to commute following elements which are used in the proof.
$$1)(T-\lambda I)^pT(x)=^?T(T-\lambda I)^p(x)$$ $$2)(T-\mu I)(T-\lambda I)^{p-1}(x)=^?(T-\lambda I)^{p-1}(T-\mu I)(x)$$