The Game Doodle-Chip Consists of Moving a Marker Around a Board

Short Answer

The game Doodle-Chip consists of moving a marker around a board. Once on a square, the marker can move to any other square which is diagonal (kitty-corner) with the square occupied. Is it possible to place the marker on the board at position A, move to every other square once and only once, and end
on the square labeled B?
(a) Yes
(b) No