Let $A$ be a $n \times n$.
Let $P$ be a $A$ minor $(n-1) \times (n-1)$ with det $\neq 0$.
Let $Q$ be a $P$ minor $(n-2) \times (n-2)$ with det $\neq 0$.
Assume there are more than one $Q$ minor in $A$.
If I find that all determinants $(n-1) \times (n-1)$ "extended" from a particular Q are equal to zero can I conclude that the same will happen for every other Q, i.e. rank of $A$ will be $R = n-2$? Or should I check for every other "extended" determinants $(n-1) \times (n-1)$ from all other particular $Q$?