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Let F(alpha)=[cosalpha-sinalpha0sinalpha...

Let `F(alpha)=[cosalpha-sinalpha0sinalphacosalpha0 0 0 1]` and `G(beta)=[cosbeta0sinbeta0 1 0-sinbeta0cosbeta]` . Show that `[F(alpha)]^(-1)=F(-alpha)` (ii) `[G(beta)]^(-1)=G(-beta)` (iii) `[F(alpha)G(beta)]^(-1)=G(-beta)F(-alpha)` .

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To solve the given problem, we need to show three parts regarding the matrices \( F(\alpha) \) and \( G(\beta) \). ### Given Matrices: 1. \( F(\alpha) = \begin{bmatrix} \cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1 \end{bmatrix} \) 2. \( G(\beta) = \begin{bmatrix} \cos \beta & 0 & \sin \beta \\ 0 & 1 & 0 \\ -\sin \beta & 0 & \cos \beta \end{bmatrix} \) ### Part (i): Show that \( [F(\alpha)]^{-1} = F(-\alpha) \) ...
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