I have taken 8 different books out of my library and still can't figure out how to do this question

SupposeXis distributedN2(μ, Σ). Determine the distribution of the random vector (X1 + X2, X1 - X2). Show that X1 + X2 and X1 - X2 are independent if Var(X1)=Var(X2)

Thanks a lot in advance!