Matrices And Determinants

If \(A = \left( {\matrix{ {{1 \over {\sqrt 5 }}} & {{2 \over {\sqrt 5 }}} \cr {{{ - 2} \over {\sqrt 5 }}} & {{1 \over {\sqrt 5 }}} \cr } } \right)\), \(B = \left( {\matrix{ 1 & 0 \cr i & 1 \cr } } \right)\), \(i = \sqrt { - 1}\), and Q = A^TBA, then the inverse of the matrix A Q²⁰²¹ A^T is equal to :