Algumas luminescências sobre o jogo Lights Out

The theory behind the Lights Out game has been developed by several authors. The aim of this work is to present some results related to this game using Linear Algebra. We establish a criterion for the solubility of this game in the case of an $m$ by $n$ grid, which depends on the invertibility of a matrix, and we present the conditions for this to occur, easily verifiable from $m$ and $n$. Furthermore, we explicitly determine the value of the determinant for a particular case.