GATE 2016 EE – SET 2 – Question 7

Given, $$P^{3}=P$$

Let $$\lambda$$ be an eigen value of P

$$\lambda ^{3}=\lambda $$  $$\Rightarrow$$   $$\lambda ^{3}-\lambda =0$$   $$\Rightarrow \lambda (\lambda ^{2}-1)=0$$

Therefore, $$\lambda =0, \pm 1$$

So the eigenvalues are 0, 1, -1