15 Quaternion Group

#todo/school : Do problem 1 📅 2025-01-15 ✅ 2025-01-15

1

Question

Compute the order of each of the elements in $Q_{8}$ (see Quaternion Group)

Proof

$| 1 | = 1$ by definition.
$| - 1 | = 2$ since $(- 1)^{2} = 1$
$| i | = | j | = | k | = 4$ since all, by definition follow this format:

i^{2} = - 1 \Rightarrow i^{4} = 1

Similarly $| - i | = | - j | = | - k | = 4$ still.
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