Question

If a skew-symmetric matrix of order $2\times 2$ is formed with zero and cube roots of unity, then the determinant of such matrices formed can be

• A. $0$
• B. $1$
• C. $\omega$
• D. ${\omega }^2$

Answer 1

Answer: (B), (C), (D)

${\omega }^2$

From given condition, only possible matrix is $\left[\begin{array}{cc}0& b\\ -b& 0\end{array}\right]$ or $\left[\begin{array}{cc}0& -b\\ b& 0\end{array}\right]$
$\therefore$ Determinant of matrix is $b^2,$ (where $b=$ cube root of unity)
When $b=1;$ Determinant $=1^2=1$
When $b=\omega ;$ Determinant $={\omega }^2$
When $b={\omega }^2;$ Determinant $={\omega }^4=\omega$