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Let $P$ be a $n \times n$ matrix such that $P^{k}=\mathbf{0}$, for some $k \in \mathbb{N}$ and where $\mathbf{0}$ is an all zeros matrix. Then at least how many eigenvalues of $P$ are zero

  1. $1$
  2. $n-1$
  3. $n$
  4. $0$
  5. None of the above
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