Question: (a) Prove that a Jordan block matrix J0,n with zero diagonal entries is nilpotent. as in Exercise 1.3.13. (b) Prove that a Jordan matrix is

(a) Prove that a Jordan block matrix J0,n with zero diagonal entries is nilpotent. as in Exercise 1.3.13.
(b) Prove that a Jordan matrix is nilpotent if and only if all its diagonal entries are zero.
(c) Prove that a matrix is nilpotent if and only if its Jordan canonical form is nilpotent.
(d) Explain why a matrix is nilpotent if and only if its only eigenvalue is 0.

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