ambidexterity n.

word-forming element making abstract nouns from adjectives and meaning "condition or quality of being ______," from Middle English -ite, from Old French -ete (Modern French -ité) and directly from Latin -itatem (nominative -itas), suffix denoting state or condition, composed of -i- (from the stem or else a connective) + the common abstract suffix -tas (see -ty (2)).

Roughly, the word in -ity usually means the quality of being what the adjective describes, or concretely an instance of the quality, or collectively all the instances; & the word in -ism means the disposition, or collectively all those who feel it. [Fowler]

word-forming element meaning "both, on both sides," from Latin ambi- "around, round about" (before vowels amb-, also sometimes reduced to am-, an-), from PIE root *ambhi- "around," which is probably an ablative plural (*ant-bhi "from both sides") of *ant- "front, forehead."