question about determinant variety in Karen Smith's "An Invitation to Algebraic Geometry"

Question

I don't understand in the example below:

If $k \geq n$, then the determinant variety is the whole space ?

Answer 1

An $n \times n$ matrix has $n$ rows and $n$ columns. The rank of a matrix is the number of linearly independent rows or columns (row rank and column rank being the same). The greatest possible number of linearly independent vectors out of a set of $n$ vectors is obviously $n$. Thus for $k \ge n$, every $n \times n$ matrix $A$ satisfies

$\text{rank}(A) \le n \le k. \tag 1$

Answer 2

Every $n \times n$ matrix has rank at most $n$.