Question: A square matrix A is called nilpotent if Ak = O for some k ¥ 1 (a) Show that is nilpotent. (b) Show that any

A square matrix A is called nilpotent if Ak = O for some k ‰¥ 1
(a) Show that

is nilpotent.
(b) Show that any strictly upper triangular matrix is nilpotent.
(c) Find a nilpotent matrix which is neither lower nor upper triangular.

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