Consider the matrix $f(x) = \begin{bmatrix} \cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{bmatrix}$. 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:

• A
  Statement $I$ is false but Statement $II$ is true.
• B
  Both Statement $I$ and Statement $II$ are false.
• C
  Statement $I$ is true but Statement $II$ is false.
• D
  Both Statement $I$ and Statement $II$ are true.