Definition of pat adverb from the Oxford Advanced Learner's Dictionary

 

pat

 adverb
adverb
BrE BrE//pæt//
 
; NAmE NAmE//pæt//
 
 
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Word Originadverb late 16th cent.: related to pat (verb); apparently originally symbolic: a frequently found early use was hit pat (i.e. hit as if with flat blow).Idioms
have/know something off pat(British English)(North American English have/know something down pat)
 
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to know something perfectly so that you can repeat it at any time without having to think about it He had all the answers off pat.
(especially North American English) to refuse to change your mind about a decision you have made or an opinion you have
See the Oxford Advanced American Dictionary entry: pat