If \({\rm{f}}\left( {\rm{x}} \right) = \left[ {\begin{array}{*{20}{c}} {\cos {\rm{x}}}&{ - \sin {\rm{x}}}&0\\ {\sin {\rm{x}}}&{\cos {\rm{x}}}&0\\ 0&0&1 \end{array}} \right]\), then which of the following are correct?
1. f(θ) × f(ϕ) = f(θ + ϕ)
2. The value of the determinant of the matrix f(θ) × f(ϕ) is 1
3. The determinant of f(x) is an even function.
Select the correct answer using the code given below:
1
1 and 2 only
2
2 and 3 only
3
1 and 3 only
4
1, 2 and 3