Consider an operator of the form [ \hatA}=r_x} \sigma^x}+r_y} \sigma^y}+r_z} \sigma^z} ] where r_x}²}+r_y}²}+r_z}²}=1 . Compute the operator A²} and find its eigenvectors. Which of the following options correctly describes the operator A²} ?

A) A²} = r_x}²} \sigma^x}+r_y}²} \sigma^y}+r_z}²} \sigma^z}
B) A²} = r_x}²} \sigma^x}+r_y}²} \sigma^y}+r_z}²} \sigma^z}+2r_x}r_y} \sigma^xy}+2r_x}r_z} \sigma^xz}+2r_y}r_z} \sigma^yz}
C) A²} = r_x}²} \sigma^x}+r_y}²} \sigma^y}+r_z}²} \sigma^z}+2r_x}r_y} \sigma^xy}+2r_x}r_z} \sigma^xz}+2r_y}r_z} \sigma^yz}+r_x}r_y}r_z} \sigma^xyz}
D) A²} = r_x}²} \sigma^x}+r_y}²} \sigma^y}+r_z}²} \sigma^z}+2r_x}r_y} \sigma^xy}+2r_x}r_z} \sigma^xz}+2r_y}r_z} \sigma^yz}+r_x}r_y}r_z} \sigma^xyz}+r_x}r_y} \sigma^yz}+r_x}r_z} \sigma^xy}+r_y}r_z} \sigma^xz}