CSIR UGC NET June 2019 Part B Question 28

Question

Let $P_{A}(x)$ denote the characteristic polynomial of a matrix $A$. Then for which of the following matrices, $P_{A}(x)-P_{A^{-1}}(x)$ is a constant?

1. $\left(\begin{array}{ll}3 & 3 \\ 2 & 4\end{array}\right)$

2. $\left(\begin{array}{ll}4 & 3 \\ 2 & 3\end{array}\right)$

3. $\left(\begin{array}{ll}3 & 2 \\ 4 & 3\end{array}\right)$

4. $\left(\begin{array}{ll}2 & 3 \\ 3 & 4\end{array}\right)$