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GATE 2019 EE – Question 12

Engineering Mathematics · Linear Algebra: Eigen values, Eigen vectors · 1 mark · Multiple choice

$M$ is a $2\times2$ matrix with eigenvalues 4 and 9. The eigenvalues of $M^2$ are

  1. 4 and 9
  2. 2 and 3
  3. $-2$ and $-3$
  4. 16 and 81

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Correct answer: (D) 16 and 81

Explanation

If $\lambda$ is an eigenvalue of $M$, then $\lambda^2$ is an eigenvalue of $M^2$, so the eigenvalues are $16$ and $81$.