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Question: recall that a square matrix a is nilpotent if ak...

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  1. Recall that a square matrix A is nilpotent if Ak = O for some k ∈ N. SupposeA and B be similar matrices.

    (a) Show that if A is nilpotent, then B is nilpotent.

    (b) Suppose k is the smallest natural number with Ak = O (such a k is called the index of nilpotence). Show that k is the smallest natural number with B = O.

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