NIELIT 2021 Dec Scientist B - Section B: 58

Question

The determinant of matrix $\begin{bmatrix} 0&p-q &p-r \\ q-p&0 &q-r \\ r-p&r-q &0 \end{bmatrix}$ is ____________ .

• A. $0$
• B. $(p-q)(q-r)(r-p)$
• C. $pqr$
• D. $3pqr$

Answer 1

$\begin{bmatrix} 0& p-q &p-r \\ -(p-q)&0 &q-r \\ -(p-r)&-(q-r) & 0 \end{bmatrix}$

 

Represent skew symmetric matrix of odd order, hence determinant is Zero.

Option A is correct