For X ~ multinomial (n,p), n is in natural numbers, p'p=1, p>0

I wonder Expected value of X is just simply np and Variance of X is np(1-p).
I know that multinomial dist has a similar idea with bernoulli dist but finding E(X) and Var(X) were a little bit confusing me

Also, if I let W be AX, then how do I find a non-singular A belongs the n * n matrices for which var W(=AX) = n(I-e1e'1) and Expected value of W?
(this question... I tried but... I failed)

I need helps!!!