GATE 2016 CS – Question 15
Two eigenvalues of a $3 \times 3$ real matrix $P$ are $(2 + \sqrt{-1})$ and 3. The determinant of $P$ is ________.
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Correct answer: 15
Explanation
A real matrix has complex eigenvalues in conjugate pairs, so the third eigenvalue is $2 - \sqrt{-1}$. The determinant is the product of the eigenvalues: $(2 + i)(2 - i)(3) = 5 \times 3 = 15$.