please answer with explanation

Let the ket vectors lui), lu2), lu3), and [us) be orthonormal basis vectors in the four-dimensional Hilbert space of some quantum system. In this problem we are concerned with the following four observables: A = (lu1) (ull + 122) (221 - 123) (231 - 124) (241) /2 B = (lu1) (21 1 - 1262) (2621 + 123) (231 - 124) (241) /2 C = A+ B= \\u1)(ull -lus>