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Question 250017
JEE Mathematics · Hard

Matrices and Determinants: JEE Advanced MCQ

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JEE AdvancedHardQuestion 250017

Question

If A² = A (idempotent), then the eigenvalues of A are:
  1. A
    0 or 1
    Correct
  2. B
    1 or −1
  3. C
    0 or −1
  4. D
    Only 1

Correct answer

0 or 1

Explanation

If λ is an eigenvalue of A with eigenvector v: Av = λv → A²v = λ²v. But A² = A → Av = λv → λ²v = λv → λ(λ−1)v = 0. Since v ≠ 0: λ = 0 or λ = 1.

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