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