CIIM 2025 Problem 5

Day 2

Sea $n$ un entero positivo. En el espacio de matrices $n \times n$ con entradas reales, considere el subconjunto $M_n$ de las matrices con entradas en el conjunto $\{-1, 1\}$ . Demuestre que al menos el 25% de las matrices en $M_n$ es invertible.

Official text Iberoamerican Interuniversity Mathematics Competition 2025 official paper, page 1. Quoted with source.

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