How to prove the independence of the functions of two random variables distributed with multivariate normal.

Question

I have to prove this statement on one of my problem sets:

If X1 and X2 are independent random variables, both distributed as N (0,1), then X1+X2 and X1−X2 are independent random variables.

I know that I have to use the properties of the multivariate normal distribution, but I don't know how to.

Thank you in advance.