If \({\rm{A}} = \left[ {\begin{array}{*{20}{c}} {\cos {\rm{\theta }}}&{\sin {\rm{\theta }}}\\ { - \sin {\rm{\theta }}}&{\cos {\rm{\theta }}} \end{array}} \right]\), then what is A3 equal to?

• A. \(\left[ {\begin{array}{*{20}{c}} {\cos 3{\rm{\theta }}}&{\sin 3{\rm{\theta }}}\\ { - \sin 3{\rm{\theta }}}&{\cos 3{\rm{\theta }}} \end{array}} \right]\)
• B. \(\left[ {\begin{array}{*{20}{c}} {{{\cos }^3}{\rm{\theta \;}}}&{{{\sin }^3}{\rm{\theta }}}\\ { - {{\sin }^3}{\rm{\theta }}}&{{{\cos }^3}{\rm{\theta }}} \end{array}} \right]\)
• C. \(\left[ {\begin{array}{*{20}{c}} {\cos 3{\rm{\theta }}}&{ - \sin 3{\rm{\theta }}}\\ {\sin 3{\rm{\theta }}}&{\cos 3{\rm{\theta }}} \end{array}} \right]\)
• D. \(\left[ {\begin{array}{*{20}{c}} {{{\cos }^3}{\rm{\theta }}}&{ - {{\sin }^3}{\rm{\theta }}}\\ {{{\sin }^3}{\rm{\theta }}}&{{{\cos }^3}{\rm{\theta }}} \end{array}} \right]\)