Corollary 2

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

For a square matrix $X$ of finite order over a commutative ring $\mathbf{A}$ the following conditions are equivalent: (i) the rows of $X$ are linearly independent; (ii) the columns of $X$ are linearly independent; (iii) $\det X$ is not a divisor of zero in $\mathbf{A}$ .

This follows immediately from no. 3, Proposition 6 and Proposition 8 above.

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

Cited by

Nothing.

Cites

no. 3, Proposition 6
Proposition 8