How do you prove that these relations are correct $(ij = k, jk = i, \ldots)$?
I tried to prove some of them, and I could, but for example:
ik = -j -j = -1 * j = (ijk) * j = i*(j^2)*k = -1 (ik) = -ik so -j = -ik...
which is wrong, ** in which step(s) am I making the mistake?** (I am sure the error is commutativity)
Also it can proven like this (or so I have found):
ik = -j ik = (i)^-1 * k^(-1) = (ki)^-1 = (j^-1) = -j