please answer with explanation

Consider a Hilbert space {|1), |2), |3) }. An observable is represented in this space by an operator that reads, as a matrix, 0 H O A = 1 0 a Find the matrix representation of a second observable, B, so that {A, B} is a complete and compatible system of observables. B shall have two eigenvalues, 1 and -1, the eigenvalue 1 is two-fold degenerate, and state |3) is an eigenstate with eigenvalue of 1. b) Check that your { A, B } are compatible