Vector Space Axioms: Proving Axiom 1

[Dustinsfl]

Since I can't copy and paste from maple into this message w/out losing formatting, I attached a pdf with all the work. I am having trouble proving axiom 1 of two general magic square matrices added together; plus, I am not sure if my set notation is entirely correct.

 

[radou]

No matter how these matrices are defined, their entries are always elements from a certain field (the reals, for example), so they are commutative.