Consider the matrix A=(010001−k00)A = \begin{pmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ -k & 0 & 0 \end{pmatrix}A=00−k100010. For which values of kkk is AAA diagonalizable over C\mathbb{C}C?
k=0k = 0k=0
k≠0k \neq 0k=0
k=1k = 1k=1
Never diagonalizable