For a square matrix $A$ in shape $n\times n$, select $m$ row indexes and the same $m$ column indexes $(m\leq n)$ to get a square submatrix - we call it a "diagonal submatrix". The question is, if for a square matrix $A$, each of its diagonal submatrices is of full rank, then what special property would $A$ have?
For example, if $A$ is a diagonal matrix (with only diagonal entries non-zero), then $A$ satisfies the above requirements.