Let with . Then there exists unique matrix such that AB=BA=det(A)I and B has integer entries.

Help me to prove this.

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- Dec 5th 2008, 01:20 PMdimukmatrix question
Let with . Then there exists unique matrix such that AB=BA=det(A)I and B has integer entries.

Help me to prove this. - Dec 5th 2008, 04:33 PMNonCommAlg
the matrix is the adjugate of the proof of can be found in any linear algebra textbook. the only thing that i have to add here is that if

then from the definition of the adjugate matrix, it's clear that as well. so i don't know why your problem says ? we also don't need to have

**Edit**: just realized that we want a unique in this case, the condition will take care of that. - Dec 5th 2008, 10:46 PMdimukmatrix question
I think that is for uniqueness of B