Show that the mean and variance-covariance matrix of ps are

Question

Let {P(µ,Σ) : µ ∈ R^k, Σ ∈ M_k} be a location-scale family on R^k. Suppose that P(0,I_k) has a Lebesgue p.d.f. that is always positive and that the mean and variance-covariance matrix of P(0,Ik) are 0 and Ik, respectively. Show that the mean and variance-covariance matrix of P(µ,Σ) are µ and Σ, respectively.