MathDB
Romania District Olympiad 2005 - Grade XI

Source:

April 10, 2011
linear algebramatrixlinear algebra unsolved

Problem Statement

Let HH denote the set of the matrices from Mn(N)\mathcal{M}_n(\mathbb{N}) and let PP the set of matrices from HH for which the sum of the entries from any row or any column is equal to 11.
a)If A∈PA\in P, prove that det⁡A=±1\det A=\pm 1.
b)If A1,A2,…,Ap∈HA_1,A_2,\ldots,A_p\in H and A1A2⋅…⋅Ap∈PA_1A_2\cdot \ldots\cdot A_p\in P, prove that A1,A2,…,Ap∈PA_1,A_2,\ldots,A_p\in P.
Back to ProblemsView on AoPS