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GATE 2026 CE (CE2) – Question 11

Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors · 1 mark · Multiple choice

Matrix $A$ has the eigenvalues 1, 2, and 3. The Trace of $A^2$ is

  1. 6
  2. 14
  3. 20
  4. 8

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Correct answer: (B) 14

Explanation

If the eigenvalues of $A$ are 1, 2 and 3, the eigenvalues of $A^2$ are $1^2$, $2^2$ and $3^2$. The trace is the sum of the eigenvalues, so $\text{tr}(A^2) = 1 + 4 + 9 = 14$.