Which of these muscles is crucial for breathing?

From a functional point of view, there are three groups of respiratory muscles: the diaphragm, the rib cage muscles, and the abdominal muscles. Each group acts on the chest wall and its compartments, i.e. the lung-apposed rib cage, the diaphragm-­apposed rib cage, and the abdomen. Contraction of the diaphragm expands the abdomen and the lower part of the rib cage (abdominal rib cage). The rib cage muscles, including the intercostals, the parasternals, the scalene, and the neck muscles, mostly act on the upper part of the rib cage (pulmonary rib cage) and are both inspiratory and expiratory. The abdominal muscles act on the abdomen and the abdominal rib cage and are expiratory.

Source: National Library of Medicine