Proposition 14

Tag 064R, permanent. Cite it as [Bourbaki, Tag 064R].

For a homogeneous linear system of $n$ equations in $n$ unknowns over a commutative ring to admit a non-zero solution, it is necessary and sufficient that the determinant of its matrix be a divisor of zero.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.