GATE 2016 EE (EE2) – Question 17
A 3×3 matrix P obeys $P^3=P$. Which listed eigenvalue triple is admissible?
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Correct answer: (A) 1,1,−1; (D) 0,1,−1
Explanation
If Pv=λv for a nonzero eigenvector, P³v=λ³v. The matrix identity therefore imposes λ³=λ, or λ(λ−1)(λ+1)=0.
Every eigenvalue must belong to {0,1,−1}, but repeats are allowed. Both (1,1,−1) and (0,1,−1) satisfy the condition, as diagonal examples demonstrate.
**The official key accepts A OR D as alternative single answers.** Neither complex triple is admissible.