If F( ) = [ * 20 c & - &0 & &0 0&0&1 ] and G ,( ) = [ * 20 c &0& … - Vidyadip

MCQ

If $F(\alpha ) = \left[ {\begin{array}{*{20}{c}}{\cos \alpha }&{ - \sin \alpha }&0\\{\sin \alpha }&{\cos \alpha }&0\\0&0&1\end{array}} \right]$ and $G\,(\beta ) = \left[ {\begin{array}{*{20}{c}}{\cos \beta }&0&{\sin \beta }\\0&1&0\\{ - \sin \beta }&0&{\cos \beta }\end{array}} \right]$, then ${[F(\alpha )\,G(\beta )]^{ - 1}} = $

A
$F(\alpha )\, - G(\beta )$
B
$ - F(\alpha )\, - G(\beta )$
C
${[F(\alpha )]^{ - 1}}\,{[G(\beta )]^{ - 1}}$
✓
${[G(\beta )]^{ - 1}}{[F(\alpha )]^{ - 1}}$

✓

Answer

Correct option: D.

${[G(\beta )]^{ - 1}}{[F(\alpha )]^{ - 1}}$

d
(d) Since ${(AB)^{ - 1}} = {B^{ - 1}}{A^{ - 1}}$.

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