# Homework Help: Rank, Co-factor matrices.

1. Apr 1, 2012

### harvesl

1. The problem statement, all variables and given/known data

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 $rankA \leq n-2$

2. Relevant equations

3. 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.

2. Apr 1, 2012

### 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?