I have a matrix $B$ of size $m$-by-$n$, where $m \gg n$. I would like to pick $m$ linearly independent rows from it and use those to form a matrix that is guaranteed to have an inverse.
I am struggling to figure out how to find these rows.
Another answer seems to imply that, in reduced row echelon form, any row of $RREF(B)$ with a leading 1 implies the same row of $B$ is linearly independent from the others in $B$, but this couldn't possibly be true, since row $RREF_i(B)$ captures information about potentially many rows of $B$, and it's not necessarily true that the independence comes from $B_i$.
How might I find a linearly independent subset from the rows of $B$?