Multiplication of matrices E and F is G. Matrices E and G are \[{\text{E}} \equiv \left[ {\begin{array}{*{20}{c}} {\cos \theta }&{ - \sin \theta }&0 \\ {\sin \theta }&{\cos \theta }&0 \\ 0&0&1 \end{array}} \right]{\text{and G}} \equiv \left[ {\begin{array}{*{20}{c}} 1&0&0 \\ 0&1&0 \\ 0&0&1 \end{array}} \right].\]
What is the matrix F?

A. \[\left[ {\begin{array}{*{20}{c}} {\cos \theta }&{ - \sin \theta }&0 \\ {\sin \theta }&{\cos \theta }&0 \\ 0&0&1 \end{array}} \right]\]

B. \[\left[ {\begin{array}{*{20}{c}} {\cos \theta }&{\cos \theta }&0 \\ { - \cos \theta }&{\sin \theta }&0 \\ 0&0&1 \end{array}} \right]\]

C. \[\left[ {\begin{array}{*{20}{c}} {\cos \theta }&{\sin \theta }&0 \\ { - \sin \theta }&{\cos \theta }&0 \\ 0&0&1 \end{array}} \right]\]

D. \[\left[ {\begin{array}{*{20}{c}} {\sin \theta }&{ - \cos \theta }&0 \\ {\cos \theta }&{\sin \theta }&0 \\ 0&0&1 \end{array}} \right]\]

Answer: Option C