Quaternions representing rotations unclear

So far i could follow the Rotation section along. In the video “Quaternion Rotation Part 1” at about 3:50 gary says that i * j results in j moving to k. I understand the result being k which is a lookup in the table (left column * top row). But why does this represent a rotation from j to k and not from i to k. Thats unclear to me as there is no explanation about this.

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