Matrices and Determinants: JEE Main 2024 Mathematics question

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 :