John Gill Commentary Luke 1:40

"and entered into the house of Zacharias and saluted Elisabeth." — Luke 1:40 (ASV)

And entered into the house of Zacharias , &c] Which was in the above city, and might be well known to her: and saluted Elisabeth; not Zacharias; either because he was not at home; or because he was deaf and dumb, and could neither hear her salutation, nor return it; or because it was not usual for women to salute men, nor men to salute women; (See Gill on Luke 1:29), yet one woman might salute another; and especially Mary saluted Elisabeth, because she came to pay the visit to her, and it was with her she was principally concerned.