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# With quaternions, please verify each area in the multiplication table, with the rule: i^2=j^2=k^2=ijk=-1?

can you please verify each component of the multiplication table, wikipedia shows one example and i need to verify the remainder equations of the multiplication table similarly. the multiplication table is as follows:

ij = k, jk = i, ki = j,

ji = -k, kj = -i, ik = -j

### 1 Answer

- Phineas BoggLv 61 decade agoFavorite Answer
Here is the first one in detail:

ij =

i * j * 1 =

i * j * -1 * -1 =

i * j * k * k * -1 =

-1 * k * -1 =

k^5 =

k * k^4 =

k * (-1)^2 =

k * 1 = k

jk = i, ki = j, are exactly the same

Here is the 4th one in detail:

ji =

k^4 * j * i =

k^4 * j * i * -1 * -1 =

k^3 * kji * ijk * -1 =

k^3 * kjj * jjk * -1 =

k^3 * k^3 * k^3 * k^2 =

k^11 =

k^2 * k =

-k

The last two are exactly the same.