- #1

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i also know that T

^{i+1}= TT

^{i}for all i >= 1 Suppose rank(T) = rank(T

^{2})

for i>= 1 Let Ui : Im(T)-->Im(T) be defined as the restriction of T

^{i}to the subspace Im(T) of V. Show Ui is nonsingular for all i

I have no idea what this question is asking or how to attempt it!