It is more interesting when White plays first. White ataris to increase the liberties, followed by the hane at to prevent Black from making two eyes in the corner. Note that White can throw in at a any time, so the eye at a has effectively only one liberty.
The correct move is Black , which may be a blind spot for some. It prevents White from creating a ko there. Up to Black , White is unable to make the approach move at a due to a shortage of liberties. This is a typical case of a capturing race where the group that has an eye kills a group that has no eye.
White and here are tricky: it actually attempts to make a seki. The throw in at destroys the possibility of White making an eye there, and is the only correct move. If White is played at , Black will play at .
here would be a careless mistake. Note that captures three White stones, so there is no ko.
Conclusion: The two marked White stones in the question are dead.