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

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

Show |A~| = |A| , A~ = adjoint A, |A| = det A

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

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.

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