If AAA is a 3×33 \times 33×3 matrix such that tr(A)=0\text{tr}(A) = 0tr(A)=0, tr(A2)=0\text{tr}(A^2) = 0tr(A2)=0, and tr(A3)=0\text{tr}(A^3) = 0tr(A3)=0, what can we conclude about AAA?
AAA is the identity matrix
AAA is a nilpotent matrix
AAA is an orthogonal matrix
AAA is a projection matrix