"that cannot be discovered by searching, mysterious," c. 1500, from Late Latin inscrutabilis, from in- "not, opposite of" (see in- (1)) + *scrutabilis, from scrutari "examine, ransack" (see scrutiny). Related: Inscrutably; inscrutableness.
word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."
In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.
early 15c., "the formal enumerating of the votes in an election to an office or dignity" (according to OED, "Now chiefly in Canon Law"), from Late Latin scrutinium "a search, inquiry" (in Medieval Latin, "a mode of election by ballot"), from Latin scrutari "to examine, investigate, search" (from PIE root *skreu- "to cut; cutting tool;" see shred (n.)). The meaning "close investigation or examination" is recorded from c. 1600.
Perhaps the original notion of the Latin word is "to search among rubbish," via scruta (plural) "trash, rags, rubbish" ("shreds"); or the original sense might be "to cut into, scratch."