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Let a matrix $A=0$. Can I say $A$ is nilpotent? I am asking if the zero matrix is nilpotent or not. Nilpotent means that $A^k = 0$ for some $k$ that is a non-negative integer. When $k = 1$, $A^k = A = 0$. Does this idea support that a zero matrix is nilpotent?

plop
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user133085
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1 Answers1

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Sure, the zero matrix $0$ is nilpotent since any of its powers is again the zero matrix. Just a side note: This question would be more suitable at the math stackexchange.

Watercrystal
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