Suppose v (a vector) is a solution to Ax=0, and Q is an element of the reals. Show Qv is also a solution.

I went about this by saying that Av = 0 (by the equation), and that A(Qv) = Av + Av + Av + Av + .... up to Q times, which = 0 + 0 + 0 + 0 + ... = 0

I don't think this is a proper way of proving this fact, though...can anyone point me in the right direction?