Quaternion Group Multiplication Table

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SUMMARY

The discussion focuses on constructing the multiplication table for the quaternion group, specifically addressing the non-commutative nature of quaternion multiplication. The key equations established are i² = j² = k² = ijk = -1. The user seeks clarification on the product ji, questioning how to derive the result when post-multiplying ji by ijk. The correct result for ji is derived from the properties of quaternion multiplication, confirming that ji = -k.

PREREQUISITES
  • Understanding of quaternion algebra and its properties
  • Familiarity with non-commutative multiplication
  • Basic knowledge of group theory
  • Experience with mathematical notation and operations
NEXT STEPS
  • Study the properties of quaternion multiplication in detail
  • Learn about the structure of non-abelian groups
  • Explore applications of quaternions in 3D rotations
  • Investigate the relationship between quaternions and complex numbers
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Mathematics students, educators, and anyone interested in group theory and quaternion algebra will benefit from this discussion.

LagrangeEuler
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Homework Statement


Obtain multiplication table for quaternion group.


Homework Equations



##i^2=j^2=k^2=ijk=-1##

The Attempt at a Solution



I have problem with elements for example ##ji## in the table. For example when I have ##ij## I say
##ijk=-1## and ##k^2=-1## so ##ij=k##. But what in the case of ##ji##? I do not know how to obtain this result.
 
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What do you get if you post-multiply (ji) by (ijk)?
 
Tnx!
 

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