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1. An nxn matrix A is said to be nilpotent if A^k = O (the zero matrix) for some positive integer k. Show that all the eigen values of a nilpotent matrix are O.
Suppose A is a nilpotent matrix. By definition, there exists some positive integer k, such that A^k=0.
Now suppose c ...
This solution is comprised of a detailed explanation to show that all the eigen values of a nilpotent matrix are O.