Quaternion Group Multiplication Table

[LagrangeEuler]

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.

 

[D H]

What do you get if you post-multiply (ji) by (ijk)?

 

[LagrangeEuler]

Tnx!