Using All 10 terms of Vector Space definition, determine if it is a vector space or not. if it is please use all terms and explain all terms. thanks

Vector space 1.1 Definition A vector space (over R) consists of a set V along with two operations '+' and '' subject to the conditions that for all vectors V, w, u e V, and all scalars r, s E R: 1) the set V is closed under vector addition, that is, V + WEV 2) vector addition is commutative v + w = w.+ v 3) vector addition is associative (v + w) tu = v+ (w+ u) 4) there is a zero vector 0 E V such that v + 0 = v for all ve V 5) each VE V has an additive inverse we V such that w + v = 0 6) the set V is closed under scalar multiplication, that is, r . V E V 7) scalar multiplication distributes over addition of scalars (r + s) . V= r . V +s . V 8) scalar multiplication distributes over vector addition r . (v + w) =r . v+r. w 9) ordinary multiplication of scalars associates with scalar multiplication (TS) . V= r . (s . V) 10) multiplication by the scalar 1 is the identity operation 1 . V = V.(1) The set of all 2 x 2 matrices of the form below (2 x 2 diagonal matrices) with usual addition and scalar multiplication of matrices. a1 0 0 where a1, a2 are arbitrary real numbers