option D
given P3=P
=> P(P2-I)=0
=> |P|=0 and |P2-I|=0 (if multiplication of 2 matrix is 0,then determinant of individual 2 matrixes are 0)
|P|=0 => so one eigen value of P is 0.
|P2-I|=0 => so one eigen value of P2 is 1.We know that if λ is eigen value of P,then λ2 is eigen value is P2.Here λ2=1.So λ=1 and λ = -1.
so 3 eigen values are 0,1,-1