These are the laws for handling of quaternions, outlined briefly under that node, but they need a bit more explanation. i, j and k are three unique roots of -1, so:
i² = j² = k² = -1 = ijk
A bit of thought reveals that multiplying the three units in any order produces -1. However, in general, one must remember that multiplication is non-commutative for quaternions:
ij = k jk = i ki = j
ji = -k kj = -i ik = -j
That's all you need to know! Impress all your friends as you manipulate quaternions with ease.