If V is a finite dimensional vector space, T: V ---> V is a
linear transformation such that T^3 - 3T^2 + 3T - I = O, where
O: V ---> V, O(v) = 0 for all v in V.
(1) Show that there is a v≠0 in V such that T(v) = v.
(2) Show that T is invertible.
1 1 0
(3) Let A = ( 0 1 1 ). Show that A is invertible, and express
0 0 1
A^{-1} as a polynomial in A with real coefficients.
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