How Does the Rank of a Matrix Influence Its Cofactor Matrix Becoming Zero?

[harvesl]

Homework Statement

Let A be an n x n matrix where $n \geq 2$. Show that $A^{\alpha} = 0$ (where $A^{\alpha}$ is the cofactor matrix and 0 here denotes the zero matrix, whose entries are the number 0) if and only if $rankA \leq n-2$

Homework Equations

The Attempt at a Solution

No idea where to start with this, it's just an additional question in the lecture notes which I haven't gone through in tutorial. Thanks.

 

[sunjin09]

The cofactor matrix is obtained by deleting rows and columns and taking the determinant. Given the rank<=n-2, what about the rank after deletion? What about the determinant?