Can a game with a unique pure strategy Nash equilibrium also have a mixed strategy equilibria?
Player 2
           +---+-------+-------+-------+
           |   |   A   |   B   |   C   |
           +---+-------+-------+-------+
Player 1   | A | (1,1) | (0,0) | (0,0) | 
           | B | (0,0) | (2,1) | (1,2) |
           | C | (0,0) | (1,2) | (2,1) |
           +---+-------+-------+-------+


If we allow $3\times 3$ games, then above is an example of the game that has exactly one pure strategy Nash equilibrium $(A, A)$ and at least one mixed strategy Nash Equilibrium.