can u answer the question with detail steps? That is the question i have

(3) Let SO(2,C) be the subgroup of SU(1,1) given by SO(2, C) = {(cm) : al =1} (a) Prove that SO(2,C) and the isotropy subgroup K of Aut(D) are isomorphic. (b) Prove that SO(2,C) is the isotropy subgroup of SU(1,1) in the sense that it consists of all matrices in SU(1,1) that leave the origin fixed. (c) Prove that SO(2, C)\SU(1,1) can be identified with the unit disk D. (The unit disk D so identified is also called the Poincar disk.) TT (3) Let SO(2,C) be the subgroup of SU(1,1) given by SO(2, C) = {(cm) : al =1} (a) Prove that SO(2,C) and the isotropy subgroup K of Aut(D) are isomorphic. (b) Prove that SO(2,C) is the isotropy subgroup of SU(1,1) in the sense that it consists of all matrices in SU(1,1) that leave the origin fixed. (c) Prove that SO(2, C)\SU(1,1) can be identified with the unit disk D. (The unit disk D so identified is also called the Poincar disk.) TT