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