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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

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