GATE IN 2024 | Question: 16

Question

A $3 \times 3$ matrix $P$ with all real elements has eigenvalues $\dfrac{1}{4}, 1$, and $-2$. The value of $\mid P^{-1}\mid$ is $\_\_\_\_\_\_$ (rounded off to nearest integer).

Answer 1

Given eigenvalues of $P$ are $1/4, 1, -2$.
Determinant $|P| = (1/4) \times 1 \times (-2) = -0.5$. \\
We know $|P^{-1}| = 1 / |P|$.
$|P^{-1}| = 1 / (-0.5) = -2$.