First slide

Applications of determinant

Question

$If F (x) = [\begin{array}{ccc} \cos x & - \sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{array}] and G (x) [\begin{array}{ccc} \cos x & 0 & \sin x \\ 0 & 1 & 0 \\ - \sin x & 0 & \cos x \end{array}] then [F (x) G (x)]^{- 1} =$

Moderate

A

$F (- x) G (- x)$
B

$F (x^{- 1}) G (x^{- 1})$
C

$G (- x) F (- x)$
D

$G (x^{- 1}) F (x^{- 1})$

Solution

$F (x) and G (x) has the property that (F (x))^{- 1} = F (- x) and (G (x))^{- 1} = G (- x)$
$\begin{array}{l} {[F (x) G (x)]}^{- 1} = G {(x)}^{- 1} F {(x)}^{- 1} \\ = G (- x) F (- x) \end{array}$

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