Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: |adj A| = |A|^(n-1), even if |A|=0 or a zero-divisor
Replies: 1   Last Post: May 3, 1999 1:20 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Bill Dubuque

Posts: 156
Registered: 12/6/04
|adj A| = |A|^(n-1), even if |A|=0 or a zero-divisor
Posted: May 2, 1999 5:54 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply



Let A be an n by n matrix over a commutative ring.

n-1
Show |A~| = |A| , A~ = adjoint A, |A| = det A

T
Note: since A A~ = |A| I, taking determinants

n
yields |A| |A~| = |A|

but |A| can't be "naively" canceled if it is 0 (or a zero-divisor).

Hint: see the next page.

-Bill Dubuque


Hint: free your mind to think universally.







Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.