Since in invertible matrices $ rank=r=m=n $ The matrix is both a square matrix and invertible from both left and right sides, left side inverse B and right side inverse C $ C=B=A^{-1} $ We end up with this equality. So when looked at the nullspace of this matrix A the only solution is zero(0) but which statement do we say 1)there is no solution or 2)the basis is zero 3)The nullspace is empty
