Hello, I have been asked to prove that three different matrices which are skew-symmetric with a defined operation can be shown to be isomorphic to the usual vectors in 3d space with the operation of the cross product.
Well the operation i guess is not so important to state as I have constructed a multiplication table for it but it is X*Y = XY-YX.
The Attempt at a Solution
I know that the cross product for a x b would be a2b3 - a3b2 etc etc and i can see in my head why it is isomorphic I just really do not know how to go about proving it. what should be vectors be, should they all be the same at just i,j,k? i don't know how to prove it without using numbers as the vectors.