Explanation

225² = 50625 ≡ 625 (mod 1000), and 625² = 390625 ≡ 625 (mod 1000), so 625 is idempotent modulo 1000. Thus 225⁴⁰ = (225²)²⁰ ≡ 625 (mod 1000). The hundreds digit of 625 is 6, option (a).