Neither is very natural. "He gave the matter some thought" or "He gave some thought to the matter" would be better.
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SheltieBitesCould:"He gave the matter a thought."be somehow grammatical, or/and have a different meaning than: "He gave the matter some thought."?No. Not that I can see. They're both grammatical, but the first just seems strange. Where did you find that wording?
she never gave a thought to being a businesswoman,emphasizes that she never gave it any