Here are the matches for Column A and Column B:
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Anterior band - E. That runs between the anterior inferior area of the medial aspect of the coronoid process of the ulna.
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Pronator teres - J. originating on the coronoid process of the ulna and inserting on the lateral surface of the radius, the pronator teres is responsible for pronation of the forearm.
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Pronator quadratus - G. This muscle originates on the radius and inserts on the ulna just proximal to the wrist.
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Supinator - B. The supinator originates on the ulna and inserts on the radius at the proximal ends of the bones on the posterior aspects.
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Posterior band - C. which does not cross the elbow joint, running between the anterior band on the coronoid process of the ulna and the posterior band on the olecranon process of the ulna.
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Brachialis - D. The brachialis muscle originates on the middle of the anterior shaft of the humerus and inserts on the coronoid process of the ulna.
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Biceps brachii - I. the biceps brachii is commonly considered a flexor of the elbow.
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Transverse band - A. running between the medial epicondyle of the humerus and the medial border of the olecranon process of the ulna.
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Brachioradialis - H. the brachioradialis muscle originates on the lateral epicondyle of the humerus and inserts on the radial styloid process.
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Biceps brachii - F. the forearm is in pronation, contraction of the biceps brachii causes the rotate externally (laterally), causing the forearm to supinate.
This should be the correct matching of the items from Column A with those in Column B.