GATE 2024 IN – Question 26
A real $3\times3$ matrix $P$ has eigenvalues $1/4,1,-2$. The determinant $|P^{-1}|$ is ______ (nearest integer).
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Correct answer: -2 to -2
Explanation
The determinant is the product of eigenvalues: $\det P=(1/4)(1)(-2)=-1/2$.
Hence $\det(P^{-1})=1/\det P=\boxed{-2}$. The vertical bars indicate determinant.