Explanation:

Multiplicative Group:
A multiplicative group is a set of elements together with an operation (usually denoted as *) that satisfies the following properties:
1. Closure: For any two elements a and b in the set, their product a * b is also in the set.
2. Associativity: For any three elements a, b, and c in the set, the product (a * b) * c is equal to a * (b * c).
3. Identity Element: There exists an element e in the set such that for any element a in the set, the product a * e is equal to a.
4. Inverse Element: For any element a in the set, there exists an element a^-1 in the set such that the product a * a^-1 is equal to the identity element e.

Givens:
The given multiplicative group IfG = {1, -1, i, -i} consists of four elements: 1, -1, i, and -i.

Order of an Element:
The order of an element in a group is the smallest positive integer n such that raising the element to the power n gives the identity element.

Determining the Order of -i:
To determine the order of -i in the multiplicative group IfG, we need to find the smallest positive integer n such that (-i)^n = 1.

Calculating the powers of -i:
(-i)^1 = -i
(-i)^2 = -1
(-i)^3 = i
(-i)^4 = 1

From the calculations, we can see that (-i)^4 = 1, which means that the order of -i is 4.

Therefore, the correct answer is option D, which states that the order of -i is four.