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Matthews (shoulder) threw a live batting practice session Tuesday, Dan Hayes of The Athletic reports.

It's the first time Matthews has faced hitters since he was diagnosed in early June with a moderate subscapularis strain in his right shoulder. If he bounces back well from Tuesday's session, Matthews could be cleared for a rehab assignment. Given that he hasn't pitched in more than a month, the 25-year-old is sure to require at least a couple rehab starts before the Twins consider putting him back into their rotation.

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