My brother and I. That is good grammar. It is because "I" is used for the subject of a sentence. "Me" is only used as an object. "Give the ball to me". "Don't hit me." "Leave me alone". So if you knock on a door and someone says "Who is there?" you would say "It is I." Do not say "It is me." or "Me." If you do then people will think you are uneducated, and you are showing that you are willing to become educated.

Yeah same as above the better sentence is "My brother and I are good tennis players" A little trick for deciding between I and Me when it is you and another is cut the sentence in half. For example in "You and me should have dinner" vs "You and I should have dinner." if you separate the two parts into: Me should have dinner and I should have dinner Makes it easier to see that "You and I should have dinner" is the better choice, although people mix this up a lot.