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What is Sternocleidomastoid muscle is supplied by: and explain in detail?
The spinal accessory nerve provides the motor supply. It passes through the muscle.
The spinal accessory nerve supplies:

The sternocleidomastoid, the chin turning
The trapezius, the shrugging muscle.

Cervical nerves provide a proprioceptive sensations to these muscles.
Reference: B D Chaurasia’s Head and Neck anatomy, 6th ed page no 384