Consider the matrix \(f(x)=\left[\begin{array}{ccc}\cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 &amp…

Consider the matrix \(f(x)=\left[\begin{array}{ccc}\cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1\end{array}\right]\).
Given below are two statements :
Statement I : \(f(-x)\) is the inverse of the matrix \(f(x)\).
Statement II : \(f(x) f(y)=f(x+y)\).
In the light of the above statements, choose the correct answer from the options given below

[JEE Main 2024, 27 Jan (Shift 1)]