GATE 2025 PI – Question 11

Engineering Mathematics · Linear Algebra · 1 mark · Multiple choice

Find the eigenvalues of $$A=\begin{pmatrix}0&-1\\1&0\end{pmatrix}.$$

$-\sqrt{-1}$ and $\sqrt{-1}$
$-1$ and $1$
$1+\sqrt{-1}$ and $1-\sqrt{-1}$
$-1+\sqrt{-1}$ and $-1-\sqrt{-1}$

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Correct answer: (A) $-\sqrt{-1}$ and $\sqrt{-1}$

Explanation

The characteristic determinant is $\det(\lambda I-A)=\lambda^2+1$. Its roots are λ = ±i, namely **−√−1 and √−1, A**.

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