On a chessboard, the king can move vertically, horizontally, or diagonally, one square at a time. Let Xn be the sequence resulting from choosing one of the king's legal moves at random. a) Is the corresponding Markov chain irreducible and/or aperiodic? b) Find, if it exists, the stationary distribution. c) Calculate the expected number of moves to return to the corner (1,1) when that was the starting point