How to detect right and left click for multiple JButtons?

Question

I am trying to make a MineSweeper game, so far I have successfully implemented a recursive tile reveal every time I click a cell. However, that is only using an ActionListener. If I wanted to be able to detect both the right and left click for each cell what do I do?

I am confused as to whether I need an ActionListener and a MouseListener for every button.

Here is my current code with an action listener:

public void actionPerformed(ActionEvent e){
    int row = 0;
    int col = 0;
    outer:
    for(row = 0; row < height; row++){
        for(col = 0; col < width; col++){
            if(e.getSource() == grid[row][col].getButton()){
                recursiveReveal(row, col);
                break outer;
            }
        }
    }
}

But what do I do to add a mouse listener for the left and right buttons for every JButton / cell?