Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and the Yahoo Answers website is now in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

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

Relevance
  • 1 decade ago
    Favorite 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.

Still have questions? Get your answers by asking now.