Math Help - quaternions

1. quaternions

Hamilton's fundamental equations are:
i squared =j sq=k sq=ijk=-1

the first part is by definition.

my question is: can the second part ie ( i j k = -1) be derived from the first part?
If so, how.
I obviously have trouble!!
many thanks for enlightening this old codger.

2. Originally Posted by ytimmer
Hamilton's fundamental equations are:
i squared =j sq=k sq=ijk=-1

the first part is by definition.

my question is: can the second part ie ( i j k = -1) be derived from the first part?
If so, how.
I obviously have trouble!!
many thanks for enlightening this old codger.
i think, ijk=-1 is part of the definition..

it is the products ij, jk, ki, etc which we can derive from these..