On the adjugate of a (0,-1,1) incidence matrix (Q797590)

The 2-adjugate matrix of a (0,-1,1) matrix N of order (\(v\times b)\) is defined to be the matrix the elements of which are the determinants of all possible 2\(\times 2\) submatrices of N, arranged in lexicographic order [see \textit{G. A. Patwardhan} and \textit{M. N. Vartak}, Combinatorics and graph theory, Proc. Symp. Calcutta 1980, Lect. Notes Math. 885, 133- 152 (1981; Zbl 0482.05017); J. Comb. Theory, Ser. A 11, 11-26 (1971; Zbl 0228.05012)]. The authors use the technique of 2-adjugation to a design whose incidence matrix has elements 0,-1,1. They investigate properties of such designs and give their applications to the balanced orthogonal designs \([v,v(v-1),2(v-1),2,2]\) [see \textit{M. B. Rao}, Partially balanced designs with unequal block sizes, J. Indian Statist. Assoc. 5, 90-103 (1967)].