Consider the matrix $f ( x ) = \left[ \begin{array} { c c c } \cos x & - \sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{array} \right]$. 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 (1) Statement I is false but Statement II is true (2) Both Statement I and Statement II are false (3) Statement I is true but Statement II is false (4) Both Statement I and Statement II are true
Consider the matrix $f ( x ) = \left[ \begin{array} { c c c } \cos x & - \sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{array} \right]$. 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\\
(1) Statement I is false but Statement II is true\\
(2) Both Statement I and Statement II are false\\
(3) Statement I is true but Statement II is false\\
(4) Both Statement I and Statement II are true