Q. If $F(x) = \begin{bmatrix} \cos x & - \sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{bmatrix}$ and $G(y) = \ \begin{bmatrix} \cos y & 0 & \sin y \\ 0 & 1 & 0 \\ - \sin y & 0 & \cos y \end{bmatrix}$ Then $\lbrack F(x)G{( - y)\rbrack}^{- 1}$ is equal to
A) $F( - x)G( - y)$
B) $G( - y)F( - x)$
C) $F\left( x^{- 1} \right)G(y^{- 1})$
D) $G\left( y^{- 1} \right)F(x^{- 1})$
Explanation
(b)
We have,
$\left\lbrack F(x)G(y) \right\rbrack^{- 1} = \left\lbrack G(y) \right\rbrack^{- 1}\left\lbrack F(x) \right\rbrack^{- 1}$
$= G( - y)F( - x)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.