Let \(F\left(x\right)=\left[\begin{array}{lll}\cos x & -\sin x& 0\\ \sin x& \cos x& 0\\ 0& 0 &1\end{array}\right]\). Which of the following relation is satisfied by \(F\left(x\right)\).

\(F\left(x\right)+F\left(y\right)=F\left(x+y\right)\) \(F\left(x\right)-F\left(y\right)=F\left(x-y\right)\) \(F\left(x\right)F\left(y\right)=F\left(x+y\right)\) \(F\left(x\right)F\left(y\right)=F\left(xy\right)\)

\(F\left(x\right)F\left(y\right)=F\left(x+y\right)\)

Multiply \(F\left(x\right)\) and \(F\left(y\right)\) and use the trigonometric identities.