If a square matrix A is nilpotent, what is its only eigenvalue?

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Zero

A matrix is nilpotent if A^k = 0 for some integer k. Since any eigenvalue λ must satisfy λ^k = 0, the only possible eigenvalue in the complex field is zero.

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For a square matrix A that satisfies A^k = 0 for some integer k, what is the only possible eigenvalue?

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