Proof of an identity in determinants

[Abdul Quadeer]

How to prove that ||An||=|A|n2?

This property is used in my book but they did not give any explanation/proof of it.
Can someone help?

Edit: n2=n2

[tiny-tim]

Hi Abdul! :smile:

(you can do sup within sup: An2 :wink:)

It's just a special case of the general rule detAB = detA*detB. :smile:

[Abdul Quadeer]

It's just a special case of the general rule detAB = detA*detB. :smile:

here A=|An| and B=1
How does it get squared?

[tiny-tim]

Perhaps I'm misunderstanding the question :redface: …

what did you mean by ||An|| ?

[Abdul Quadeer]

double determinant of An......... Is there any other meaning?

[Abdul Quadeer]

Any idea?

[Fredrik]

I'm not familiar with the term "double determinant". Can you define it?

[Abdul Quadeer]

ehh..there is no such identity :redface:
The step is actually |adj(adjA)|=||A|n-2A|=(|A|(n-2)n)|A|.
I thought it is goes like ||A|n-2|=|A|(n-2)n, but thats wrong.
I figured out that the above property is |kA|=kn|A|, where n is the order of A.