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E-id-k-vectorial-space-and-f-L-E-1-prove-that-if-f-is-nilpotent-with-indice-p-1-I-f-is-bijective-and-I-f-1-i-0-p-1-f-i-2-let-E-R-n-x-and-f-L-E-f-p-p-p-prove-that-f-is-inver

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Question Number 37228 by abdo.msup.com last updated on 11/Jun/18
E id k vectorial space and f∈L(E) 1)prove that if f is nilpotent with indice p≥1 ,I −f is bijective and (I−f)^(−1) =Σ_(i=0) ^(p−1) f^i 2)let E=R_n [x] and f∈L(E) / f(p) =p−p^′ prove that f is inversible and find f^(−1) .
Eidkvectorialspaceandf∈L(E)1)provethatiffisnilpotentwithindicep⩾1,I−fisbijectiveand(I−f)−1=∑i=0p−1fi2)letE=Rn[x]andf∈L(E)/f(p)=p−p′provethatfisinversibleandfindf−1.

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