Arrange the following matrices in ascending order of their determinant values.A) cosθsinθ-sinθcosθB) 1ww2ww21w21wC) 0i-i0

# Arrange the following matrices in ascending order of their determinant values.A) $\left[\begin{array}{cc}\mathrm{cos}\theta & \mathrm{sin}\theta \\ -\mathrm{sin}\theta & \mathrm{cos}\theta \end{array}\right]$B) $\left[\begin{array}{ccc}1& w& {w}^{2}\\ w& {w}^{2}& 1\\ {w}^{2}& 1& w\end{array}\right]$C) $\left[\begin{array}{cc}0& i\\ -i& 0\end{array}\right]$

1. A

C,A,B

2. B

B,C,A

3. C

C,B,A

4. D

B,A,C

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### Solution:

$\left|\begin{array}{cc}\mathrm{cos}\theta & \mathrm{sin}\theta \\ -\mathrm{sin}\theta & \mathrm{cos}\theta \end{array}\right|=1$
$\left|\begin{array}{ccc}1& w& {w}^{2}\\ w& {w}^{2}& 1\\ {w}^{2}& 1& w\end{array}\right|=0$

$\left|\begin{array}{cc}0& i\\ -i& 0\end{array}\right|=-1$

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