The integer m n matrices A = (a i j ), B = (b i j ) are said to be equivalent ifa i j = u i + b i j + v j for alli = 1 m, j = 1 n, for some u 1 u m ,v 1 v n Z. For an integer matrix X the symbol S(X) denotes the set of all nonnegative integer matrices equivalent to X having a zero element in each row and each column. We develop algorithms to solve the problems of the following type for a given class S(X) : decide whether A S(X); find the largest possible value for each position among all matrices in S(X); find a matrix in S(X) with prescribed values of a specified entry or row (column); find a matrix in S(X) with term rank 2. A complete description of those S(X) containing only zero-one matrices is presented.