Hello,

It is the same as if it was numbers or whatever. Matrices are considered as vectors.

Check the rules defining a space vector :

- associative. That is [x,y]+([x1,y1]+[x2,y2])=([x,y]+[x1,y1])+[x2,y2]

- commutative. [x,y]+[x1,y1]=[x1,y1]+[x,y]

- addition has an identity element. is there [x0,y0], which belongs to the set, such that [x,y]+[x0,y0]=[x,y] ?

etc...

I think it's not a vector space because there is a problem with the multiplicative law (no identity element)