Does the Jordan Product Share Properties with the Cross Product?

dwn
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I would like to know if the Jordan Product carries along with it the same properties as that of the cross product (i.e. associativity, commutable, left/right distributive)? If you've taken LA, I'm sure you know that professors require us to complete a project and I've chosen the Jordan Product as mine. I need to show whether a Jordan Product has certain properties.

A x B = 1/2 (AB + BA) [ Jordan Product ]


For example: (A x B) x C = A x (B x C)
(A + B) x C = (A x C) + (B x C)

Should we set up our own n x n matrices and see if we arrive at the same answer?

Thank you for any assistance.
 
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