Heidegger's Bible Handbook: 1 Peter: Written in Hebrew?
5. It was written in the Greek idiom, not the Hebrew.
That this Epistle was written in the Hebrew idiom, and translated into the Greek language by Mark, some incorrectly gather out of Jerome’s Epistle 150 to Hedibia. Jerome does indeed say that the two Epistles ascribed to Peter differ in style and character, and the construction of words. But by character he indicates, not the language in which each was written, but the manner of speaking, and the propriety of speech.