Question: Let J be a Jordan matrix. (a) Prove that Jk is a complete matrix for some k 1 if and only if either J

Let J be a Jordan matrix.
(a) Prove that Jk is a complete matrix for some k ≥ 1 if and only if either J is diagonal, or J is nilpotent with Jk = O.
(b) Suppose that A is an incomplete matrix such that Ak is complete for some k ≥ 2. Prove that Ak = O. (A simpler version of this problem appears in Exercise 8.3.8.)

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