$2$ Solve these logic puzzles!

A particular island has as its inhabitants either knights, who always tell the truth, or knaves, who always lie. Everyone is either a knight or a knave and no one is both. For better or worse, you end up on this island and are confronted with $2$ inhabitants, A and B$.$ Please answer each question. Each correct answer is worth up to $10$ points. Note that for partial credit, you must show your work.

Suppose that A were to say, about herself and $B,$ "Both of us are knaves". Of what type, or types, are A and $B,$ or is it indeterminate what one or both of them are?

Suppose that A were to say, about herself and B$,"$We are both of the same type". Of what type, or types, are A and $B$ or is it indeterminate what one or both of them are?

Suppose that A were to say, of both herself and $B,$ "I am a knave or B is a knight". Of what type, or types, are A and B$,$ or is it indeterminate what one or both of them are?

Suppose that B were to say, "I am a knight unless A is the same". Of what type, or types, are A and $B,$ or is it indeterminate what one or both of them are?