Hm, for me:
n = transforms.Normalize([0.485 , 0.546, 0.406], [0.229 , 0.224 , 0.225])
n_inv = transforms.Normalize([-0.485/0.229, -0.546/0.224, -0.406/0.225], [1/0.229, 1/0.224, 1/0.225])
a = torch.randn(3,4,5) # works with real images, too
(n_inv(n(a))-a).abs().max()

gives 3e-7ish, so it is inverting up to numerical precision.
Best regards
Thomas