In the Cartesian coordinate plane, the square $ABCD$ with vertex coordinates
$$\mathrm { A } ( - 1 , - 1 ) , \mathrm { B } ( 1 , - 1 ) , \mathrm { C } ( 1,1 ) , \mathrm { D } ( - 1,1 )$$
is given below.
To this square, the following transformations are applied in order:
- Rotation counterclockwise by $45 ^ { \circ }$ about the origin, - Reflection with respect to the y-axis, - Rotation clockwise by $45 ^ { \circ }$ about the origin.
In the final state, which of the following are the vertex points of this square whose coordinates remain unchanged?
A) A and B B) A and C C) A and D D) B and C E) C and D