и туда кнопочек напихать?

   //обнулим матрицу
    for (int i=0;i<30;++i)
         for(int j=0;j<30;++j)
             matrix[i][j]=0;

memset(matrix, 0, sizeof(matrix));

Нет, тебе нужно выделить все кнопки, которые ты хочешь поместить в группу. Затем кликнуть правой кнопкой мышки и выбрать "Назначить новую группу кнопок"->"Новая группа кнопок". В коде уже использовать указатель на buttonGroup, создать слот в главном окне типа on_buttonGroup_buttonClicked(QAbstractButton * button).

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QAbstractButton * QButtonGroup::button ( int id ) const
Returns the button with the specified id, or 0 if no such button exists.

This function was introduced in Qt 4.1.

The QButtonGroup class provides a container to organize groups of button widgets.
QButtonGroup provides an abstract container into which button widgets can be placed. It does not provide a visual representation of this container (see QGroupBox for a container widget), but instead manages the states of each of the buttons in the group.
An exclusive button group switches off all checkable (toggle) buttons except the one that was clicked. By default, a button group is exclusive. The buttons in a button group are usually checkable QPushButton's, QCheckBoxes (normally for non-exclusive button groups), or QRadioButtons. If you create an exclusive button group, you should ensure that one of the buttons in the group is initially checked; otherwise, the group will initially be in a state where no buttons are checked.
A button is added to the group with addButton(). It can be removed from the group with removeButton(). If the group is exclusive, the currently checked button is available as checkedButton(). If a button is clicked the buttonClicked() signal is emitted. For a checkable button in an exclusive group this means that the button was checked. The list of buttons in the group is returned by buttons().
In addition, QButtonGroup can map between integers and buttons. You can assign an integer id to a button with setId(), and retrieve it with id(). The id of the currently checked button is available with checkedId(), and there is an overloaded signal buttonClicked() which emits the id of the button. The purpose of the mapping mechanism is to simplify the representation of enum values in a user interface.