If $P$ is a $3 \times 3$ real matrix such that $P^{T} = aP + (a-1)I$, where $a > 1$, then (1) $P$ is a singular matrix (2) $|\operatorname{Adj} P| > 1$ (3) $|\operatorname{Adj} P| = \frac{1}{2}$ (4) $|\operatorname{Adj} P| = 1$
If $P$ is a $3 \times 3$ real matrix such that $P^{T} = aP + (a-1)I$, where $a > 1$, then\\
(1) $P$ is a singular matrix\\
(2) $|\operatorname{Adj} P| > 1$\\
(3) $|\operatorname{Adj} P| = \frac{1}{2}$\\
(4) $|\operatorname{Adj} P| = 1$