# Row rank and column rank of matrix with entries in a commutative ring

Let $$RR$$ be a unital commutative ring and $$A∈Mn×m(R)A\in M_{n\times m}(R)$$. Under which appropriate invariant “rank” of modules discussed
in “Ranks of Modules”
one can say that the row rank of $$AA$$ is equal to the column rank of $$AA$$?