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Determinants equal mod 2

Source: ICMC 2022 Round 1 P3

December 4, 2021
linear algebracollege contestsDeterminantsICMC

Problem Statement

Let M\mathcal M be the set of n×nn\times n matrices with integer entries. Find all A∈MA\in\mathcal M such that det⁡(A+B)+det⁡(B)\det(A+B)+\det(B) is even for all B∈MB\in\mathcal M.
Proposed by Ethan Tan
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