Which property is true for the Hat Matrix H=X(XTX)−1XTH = X(X^T X)^{-1} X^TH=X(XTX)−1XT?
HHH is symmetric (H=HTH = H^TH=HT).
HHH is idempotent (H2=HH^2 = HH2=H).
The trace of HHH is nnn.
The eigenvalues of HHH are all zero.