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**option D **

given P^{3}=P

=> P(P^{2}-I)=0

=> |P|=0 and |P^{2}-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.

|P^{2}-I|=0 => so one eigen value of P^{2} is 1.We know that if **λ** is eigen value of P,then **λ**^{2} is eigen value is P^{2}.Here **λ**^{2}=1.So **λ=1 **and** λ = -1.**

**so 3 eigen values are 0,1,-1**