element meaning "into, in, on, upon" (also im-, il-, ir- by assimilation of -n- with following consonant), from Latin in- "in," from PIE root *en "in."
In Old French (and hence in Middle English) this often became en-, which in English had a strong tendency to revert to Latin in-, but not always, which accounts for pairs such as enquire/inquire. There was a native form, which in West Saxon usually appeared as on- (as in Old English onliehtan "to enlighten"), and some of those verbs survived into Middle English (such as inwrite "to inscribe"), but all now seem to be extinct.
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In- (2) "in" is not related to in- (1) "not," but both were common prefixes in Latin, causing confusion as in English: to the Romans impressus could mean "pressed" or "unpressed;" inaudire meant "to hear," but inauditus meant "unheard of;" in Late Latin investigabilis could mean "that may be searched into" or "that cannot be searched into." Latin invocatus was "uncalled, uninvited," but invocare was "to call, appeal to." The identical prefixes also set English words in opposition to their French twins, as in French inhabitable "uninhabitable."
In English, inflammable is commonly cited in decrying the confusion. Implume (1610s) meant "to feather," but implumed (c. 1600) meant "unfeathered." Impliable can mean "capable of being implied" (1865) or "inflexible" (1734). Infusable was "capable of being infused" but also "incapable of being fused or melted."
Impartible in 17c. could mean "incapable of being divided" or "capable of being imparted." Inanimate (adj.) is "lifeless," but Donne uses inanimate (v.) to mean "infuse with life or vigor." Irruption is "a breaking in," but irruptible is "unbreakable." Impassioned "full of passion" but impassionate "free from passion."
In addition to improve "use to one's profit," Middle English also had a verb improve meaning "to disprove" (15c.). To inculpate is "to accuse," but inculpable means "not culpable, free from blame." Infestive has meant "troublesome, annoying" (1560s, from infest) and "not festive" (1620s). In Middle English inflexible could mean "incapable of being bent" or "capable of being swayed or moved." In 17c., informed could mean "current in information," formed, animated," or "unformed, formless" ("This was an awkward use" [OED 1989]).
Inhabited has meant "dwelt in" (1560s) and "uninhabited" (1610s); inhabitable in English likewise has been used in opposite senses, and the confusion in it goes back to Late Latin. Ingenerate (adj.) is from 1530s as "generated within," 1640s as "not generated."
Immutable "not capable of change," from Latin immutabilis, shares space in English dictionaries with immute (v.) "to change into another form," from Latin immutare.
Note that in nearly all cases one or both of the crossed words is obsolete.