Question: (5) A square matrix A is called nilpotent if there exists a positive integer k such that Ak = 0 where 0 is the

(5) A square matrix A is called nilpotent if there exists a

(5) A square matrix A is called nilpotent if there exists a positive integer k such that Ak = 0 where 0 is the zero matrix. If A is nilpotent n xn matrix and B is n x n matrix such that AB = BA. (a) Show that the product AB is niloptent. [0 (b) Let A = Show that: and B i) A is nilpotent, ii) B is invertible, ii) Is (B A) invertible?, iv) Is (AB) niloptent?

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