Given AAA is a 3×33 \times 33×3 matrix such that A3=0A^3 = 0A3=0 (nilpotent). Which of the following is true?
AAA must be the zero matrix
rank(A)≤2\text{rank}(A) \leq 2rank(A)≤2
det(A)=1\det(A) = 1det(A)=1
The eigenvalues are non-zero