Commutativity and Associativity of Jordan Product

[keemosabi]

Homework Statement

A and B are n x n matrices, so their Jordan Product is (AB + BA)/2. Show that this product is commutative but not associative.

Homework Equations

The Attempt at a Solution

I understand the logic behind the answer, but I don't know how to show it. Where would I start?

 

[JeSuisConf]

/edit: deleted answer.

For associativity, just write out A*B and B*A and expand. For commutivity, write out A*(B*C) and (A*B)*C, and if what you get when you expand the two things is not the same, then you have shown what you wanted.

 

[keemosabi]

/edit: deleted answer.

For associativity, just write out A*B and B*A and expand. For commutivity, write out A*(B*C) and (A*B)*C, and if what you get when you expand the two things is not the same, then you have shown what you wanted.

Thank you so much for the help. I figured out this question and the other Jordan Product questions from your advice.