Question

Det $\left|\begin{array}{ccc}0& p-q& p-r\\ q-p& 0& q-r\\ r-p& r-q& 0\end{array}\right|$ =

• A. (p-q) (q-r) (r-p)
• B. 0
• C. pqr
• D. 4 pqr

Answer 1

The correct option is B 0

Performing $C_1\to C_1-C_2,C_2\to C_2-C_3$
$\left|\begin{array}{ccc}q-p& r-q& p-r\\ g-p& r-q& q-r\\ q-p& r-q& 0\end{array}\right|$
$(q-p)(r-q)\left|\begin{array}{ccc}1& 1& p-r\\ 1& 1& q-r\\ 1& 1& 0\end{array}\right|$
=0 {$\because$ Two columns are identical}