A( ) [ array cc & - & array ] , then [A^2( ) ]⁻¹=

Step-by-step solution

aligned & A( )= [ array cc & - & array ] | A ( )|= ^2 + ^2 =1 & ~A ^2( )= [ array cc & - & array ] [ array cc & - & array ] & [ array cc ^2 - ^2 & 2 - & ^2 - ^2 array ]= [ array cc & - & array ] & adj [ A ^2( ) ] [ array cc 2 & - 2 2 & 2 array ] & [ A ^2( ) ]⁻¹= [ array cc 2 & - 2 2 & 2 array ] [ | A ^2 |=| A |^2=1 ] & [ A ^2( ) ]⁻¹= [ array cc (-2 ) & (-2 ) - (-2 ) & (-2 ) array ]= A (-2 ) aligned