(1 0) (i0) (0 1) (0 i) (-1 0 ) (-i0) (0 -1) (0 -i)

(0 1) , (0-i), (-1 0) , (i 0), (0 -1), (0i), (1 0), (-i0)

(*they all suppose to be 2x2 matrix)

whereirefers to the imaginary number square root -1

A) prove that the set S forms a group of order 8

B) show that this group is non-abelian

c) Prove that all subgroups of this group are normal ( Hints: What are the possible subgroup orders and indexes?