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Let $A$ be an $n \times n$ matrix with real entries such that $A^{k}=0$ (0-matrix), for some $k \in \mathbb{N}$. Then

  1. $A$ has to be the $0$ matrix 
  2. Trace$(A)$ could be non-zero 
  3. $A$ is diagonalizable 
  4. $0$ is the only eigenvalue of $A$.
in Linear Algebra by Boss (29.9k points) | 85 views
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Is it B) Trace(A) could be non-zero?

Because is not bound to affect the result of exponentiation of a matrix.

1 Answer

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Matrix A is basically nilpotent matrix in case of nilpotent matrix eigen values are 0 and as it has same eigen values it is not diagonalizable . So answer is option D.
by Junior (683 points)

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