  Pairs (A,B) of mutually annihilating operators AB=BA=0 on a finite
dimensional vector space over an algebraically closed field were classified by
Gelfand and Ponomarev [Russian Math. Surveys 23 (1968) 1-58] by method of
linear relations. The classification of (A,B) over any field was derived by
Nazarova, Roiter, Sergeichuk, and Bondarenko [J. Soviet Math. 3 (1975) 636-654]
from the classification of finitely generated modules over a dyad of two local
Dedekind rings. We give canonical matrices of (A,B) over any field in an
explicit form and our proof is constructive: the matrices of (A,B) are
sequentially reduced to their canonical form by similarity transformations
(A,B)--> S^{-1}AS, S^{-1}BS).
