Two sequences \(\left[ {{\rm{a}},{\rm{\;b}},{\rm{\;c}}\left] {{\rm{\;and\;}}} \right[{\rm{A}},{\rm{\;B}},{\rm{\;C}}} \right]\) are related as,\(\left[ {\begin{array}{*{20}{c}} {\rm{A}}\\ {\rm{B}}\\ {\rm{C}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 1&1&1\\ 1&{{\rm{w}}_3^{ - 1}}&{{\rm{w}}_3^{ - 2}}\\ 1&{{\rm{w}}_3^{ - 2}}&{{\rm{w}}_3^{ - 4}} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {\rm{a}}\\ {\rm{b}}\\ {\rm{c}} \end{array}} \right]{\rm{where\;}}{{\rm{w}}_3} = {{\rm{e}}^{{\rm{j}}\frac{{2{\rm{\pi }}}}{3}}}\)If another sequence \({\rm{p}},{\rm{q}},{\rm{\;r}}\) is derived as,\(\left[ {\begin{array}{*{20}{c}} {\rm{p}}\\ {\rm{q}}\\ {\rm{r}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 1&1&1\\ 1&{{\rm{w}}_3^1}&{{\rm{w}}_3^2}\\ 1&{{\rm{w}}_3^2}&{{\rm{w}}_3^4} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} 1&0&0\\ 0&{{\rm{w}}_3^2}&0\\ 0&0&{{\rm{w}}_3^4} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {\frac{{\rm{A}}}{3}}\\ {\frac{{\rm{B}}}{3}}\\ {\frac{{\rm{C}}}{3}} \end{array}} \right]\) ,Then the relationship between the sequences \(\left[ {{\rm{p}},{\rm{\;q}},{\rm{\;r}}\left] {{\rm{\;and\;}}} \right[{\rm{a}},{\rm{\;b}},{\rm{\;c}}} \right]{\rm{\;is}}\)

• A. \(\left[ {{\rm{p}},{\rm{q}},{\rm{r}}} \right] = \left[ {{\rm{b}},{\rm{a}},{\rm{c}}} \right]\)
• B. \(\left[ {{\rm{p}},{\rm{q}},{\rm{r}}} \right] = \left[ {{\rm{b}},{\rm{c}},{\rm{a}}} \right]\)
• C. \(\left[ {{\rm{p}},{\rm{q}},{\rm{r}}} \right] = \left[ {{\rm{c}},{\rm{a}},{\rm{b}}} \right]\)
• D. \(\left[ {{\rm{p}},{\rm{q}},{\rm{r}}} \right] = \left[ {{\rm{c}},{\rm{b}},{\rm{a}}} \right]\)