Question

A : $\left|\begin{array}{ccc}0& p-e& e-r\\ e-p& 0& r-p\\ r-e& p-r& 0\end{array}\right|$ =0
R : The determinant of a skew symmetric matrix is zero
The correct answer is

• A. Both A and R are true R is correct explanation to A
• B. Both A and R are true but R is not correct explanation to A
• C. A is true R is false
• D. A is false R is true

Answer 1

The correct option is C A is true R is false

Let $A=\left[\begin{array}{ccc}0& p-e& e-r\\ e-p& 0& r-p\\ r-e& p-r& 0\end{array}\right]$
Here, $A^T=\left[\begin{array}{ccc}0& e-p& r-e\\ p-e& 0& p-r\\ e-r& r-p& 0\end{array}\right]$
$\Rightarrow A^T=-A$
Hence, A is skew-symmetric matrix of order 3.
Determinant of a skew symmetric matrix of odd order is 0.