MathematicsArrange 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) $[\begin{matrix} \cos θ & \sin θ \\ - \sin θ & \cos θ \end{matrix}]$
B) $[\begin{matrix} 1 & w & w^{2} \\ w & w^{2} & 1 \\ w^{2} & 1 & w \end{matrix}]$
C) $[\begin{matrix} 0 & i \\ - i & 0 \end{matrix}]$

A
C,A,B
B
B,C,A
C
C,B,A
D
B,A,C

Solution:

$|\begin{matrix} \cos θ & \sin θ \\ - \sin θ & \cos θ \end{matrix}| = 1$
$|\begin{matrix} 1 & w & w^{2} \\ w & w^{2} & 1 \\ w^{2} & 1 & w \end{matrix}| = 0$

$|\begin{matrix} 0 & i \\ - i & 0 \end{matrix}| = - 1$

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