Let $p, q$ and $r$ be three distinct positive real numbers. If $D=\left|\begin{array}{lll}p& q& r\\ q& r& p\\ r& p& q\end{array}\right|,$ then which one of the following is correct?

Consider the following in respect of a non-singular matrix of order $3.$

$1$. $A(adjA)=(adjA)A$

$2$. $|adjA|=\left|A\right|$

Which of the above statements is/are correct?

$\left|\begin{array}{lll}1!& 2!& 3!\\ 2!& 3!& 4!\\ 3!& 4!& 5!\end{array}\right|?$

$\left|\begin{array}{ccc}x& 0& 2\\ 2x& 2& 1\\ 1& 1& 1\end{array}\right|+\left|\begin{array}{ccc}3x& 0& 2\\ x^2& 2& 1\\ 0& 1& 1\end{array}\right|=0?$

value of $\left|\begin{array}{ccc}x+a& b& c\\ a& x+b& c\\ a& b& x+c\end{array}\right|?$