Let A be a nonzero square matrix. Is it possible that a positive integer k exist

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Let A be a nonzero square matrix. Is it possible that a positive integer k exists such that A square matrix A is nilpotent of index k when A 0 ,A^2 0,,Ak 1 = 0, but Ak = In this task you will explore nilpotent matrices. The matrix in the example given above is nilpotent. What is its index? ( 2 marks ) Use a software program to determine which of the following matrices are nilpotent and find their indices Find 3x3 nilpotent matrices of indices 2 and 3 Find 4x4 nilpotent matrices of indices 2, 3, and 4 Find nilpotent matrix of index 5 Are nilpotent matrices invertible? prove your answer When A is nilpotent, what can you say about A1 ? prove your answer Show that if A is nilpotent, then I - A is invertible

Explanation / Answer

given is true.

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