Given a set S = {1, -1, i, -i} where i2 = -1 and with multiplication...

Given a set S = {1, -1, i, -i} where i² = -1 and with multiplication * on this set,

complete the following Cayley table:

*	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.

(d) Investigate the following properties of binary operations for this operation on S:

i. Closed

ii. Identity

iii. Inverse

iv. Associativity

Solutions

Expert Solution

Colby Messinger answered 2 weeks ago

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