Two miniatures relating the 2 × 2 minors of a square matrix and the symmetric group

In the first miniature we recall a puzzle proposed by Martin Gardner in 1957 and refreshed by Blasco in 2014. We prove some properties of the matrices involved. We show that Gardner magical matrices are tropically singular. In the second miniature we construct a counterexample to the following conjecture by R. Flores: for a square matrix A = (aij ) of size n, if for each permutation σ there exists a 2 × 2 minor of A such that aσ(k)k aσ(l)l - aσ(k)l aσ(l)k vanishes, then determinant of A vanishes.