Do Babies Know Who Their Mother Is ?

Do babies know ? I mean I know people will say they obviously do but i'm asking because ever since my mom came to stay with us to help me out with our first baby , my baby (most of the time) will only sleep if she's in my mothers arms and also sometimes when I try to feed her her bottle she won't want it but once I hand her to my mom and my mom offers her the bottle , she eats it. However one time when we were visiting my husbands parents my baby started crying when my MIL had her and once I carried her and took her out the room she stopped crying .

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