Demonstrate that matrixes M(2x2) with the sum of matrixes is a vector space.

Question

I am confused. Do i need to demonstrate each propertie (distributive, associative, etc) for the sum of matrixes or I only need to prove that the sum of matrixes results into another matrix, and if so, how do I do it? Thanks for the help

Answer 1

It should be no problem to demonstrate that the sum of two 2x2 matrices is another 2x2 matrix. The definition of matrix addition guarantees it.

Just review the properties of a vector space and it should be clear that M quialifies.