Completely Non-zero Determinant

Given an integer $n$, you need to construct an n \times n matrix $M$ consisting of zeroes and ones. This matrix must satisfy the following property: for every $m$, where 1 \le m \le n, and every $a$, where 1 \le a \le n - m + 1, the sub-matrix formed by rows $1$ through $m$ and columns $a$ through a + m - 1 of $M$ is non-singular over \mathbb{F}_2.

Recall that an m \times m matrix $P$ over \mathbb{F}_2 is non-singular if there exists an odd number of permutations $p$ of the elements 1, 2, \ldots, m such that all elements P_{1, p_1}, P_{2, p_2}, \ldots, P_{m, p_m} are equal to one.