In: Advanced Math
Given a set S = {1, 1, i, i} where i^{2} = 1 and with multiplication * on this set,
* 
1 
i 
1 
i 
1 
1 
1 
i 

i 
i 
1 

1 

i 
(b) Determine whether, or not, the operation * is a binary operation on S.
(c) Is * commutative on S?
(d) Investigate the following properties of binary operations for this operation on S:
i. Closed
ii. Identity
iii. Inverse
iv. Associativity