the identity i<sup>2</sup>=j<sup>2</sup>=k<sup>2</sup>=ijk=-1

what i don't understand is the ijk part.

what i understand of it is that since quaternions are not commutative this part of the identity affects the results of quaternion multiplication but...

since i=j=k= square root (-1)

then shouldn't ijk=-i=-j=-k?

i'm obviously missing something here but i can't find what.