The group of quaternions is the group of order 8 consisting of matrices in GL(2,C) as follows Qs = {I,A,A^2,A^3,B,BA, BA^2, BA^3}, where the group operation is matrix multiplication and (A) and B = (4pts. 1). What is the index of H = (A) in Qs? Explain. (4pts. ii) List the left cosets of H = (A) in Qs. For full credit, you must list all the elements in each coset.