Rank of adjugate matrix

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.

micromass

What is [itex]A\cdot adj(A)[/itex]?? What are the implications on the rank?

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quackdesk	Rank of adjugate matrix Tweet 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.

micromass Blog Entries: 8 Recognitions: Gold Member Science Advisor Staff Emeritus	What is [itex]A\cdot adj(A)[/itex]?? What are the implications on the rank?