If \(F(x)=\left[\begin{array}{lll}\cos x & -\sin x&0\\ \sin x& \cos x&0\\ 0&0&1\end{array}\right]\) Then which of the following is true

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

\(F(x)×F(y)=\left[\begin{array}{lll}\cos x & -\sin x&0\\ \sin x& \cos x&0\\ 0&0&1\end{array}\right]\left[\begin{array}{lll}\cos y & -\sin y&0\\ \sin y& \cos y&0\\ 0&0&1\end{array}\right]\)

$=\begin{bmatrix}\cos x\cos y-\sin x\sin y&-\cos x\sin y-\sin x\cos y&0\\\sin x\cos y+\sin x\cos y&\cos x\cos y-\sin x\sin y&0\\0&0&1\end{bmatrix}$

$F(x)F(y)=\begin{bmatrix}\cos(x+y)&-\sin(x+y)&0\\\sin(x+y)&\cos(x+y)&0\\0&0&1\end{bmatrix}=F(x+y)$

so \(F(x)F(y)=F(x+y)\)