# Rank of adjugate matrix

1. Aug 23, 2012

### quackdesk

how that the rank of the adjugate matrix (r(adj(A))) is :

n if r(A)=n

1 if r(A)=n-1

0 if r(A)<n-1

How to deal with the proof? Can someone give more insight? What proof should I use here?

I have an idea only for the third statement.

2. Aug 23, 2012

### micromass

What is $A\cdot adj(A)$?? What are the implications on the rank?

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