If \(A = \left( {\begin{array}{*{20}{c}} {\frac{1}{{\sqrt 5 }}}&{\frac{2}{{\sqrt 5 }}}\\ {\frac{{ - 2}}{{\sqrt 5 }}}&{\frac{1}{{\sqrt 5 }}} \end{array}} \right),B = \left( {\begin{array}{*{20}{c}} 1&0\\ i&1 \end{array}} \right),i = \sqrt { - 1} \) and Q = ATBA, then the inverse of the matrix A Q2021 AT is equal to:
1
\(\left( {\begin{array}{*{20}{c}} 1&0\\ {-2021\,i}&1 \end{array}} \right) \)
2
\(\left( {\begin{array}{*{20}{c}} {\frac{1}{{\sqrt 5 }}}&{ - 2021}\\ {2021}&{\frac{1}{{\sqrt 5 }}} \end{array}} \right)\)
3
\(\left( {\begin{array}{*{20}{c}} 1&{ - 2021\,i}\\ 0&1 \end{array}} \right) \)
4
\(\left( {\begin{array}{*{20}{c}} 1&0\\ {2021\,i}&1 \end{array}} \right) \)