Question

If the determinant of the matrix $A=\left[\begin{array}{ccc}0& a& b\\ -a& 0& \beta \\ -b& \alpha & 0\end{array}\right]$ is zero for all $a,b$ then $\alpha +\beta =$

• A. 0
• B. 1
• C. -1
• D. 2

Answer 1

Answer: (A)

We have,
$A=\left[\begin{array}{ccc}0& a& b\\ -a& 0& \beta \\ -b& \alpha & 0\end{array}\right]$
$|A|=0$ for all $a,b$
$\therefore A$ is skew symmetric matrix.
Hence, $\alpha =-\beta \Rightarrow \alpha +\beta =0$