MathDB

B6

Part of 1986 Putnam

Problems(1)

Putnam 1986 B6

Source:

8/5/2019
Suppose A,B,C,DA,B,C,D are n×nn \times n matrices with entries in a field FF, satisfying the conditions that ABTAB^T and CDTCD^T are symmetric and ADT−BCT=IAD^T - BC^T = I. Here II is the n×nn \times n identity matrix, and if MM is an n×nn \times n matrix, MTM^T is its transpose. Prove that ATD−CTB=IA^T D - C^T B = I.
Putnam