I found this example in a book of practice problems and if someone could explain this to me, I would be really grateful:

If all entries of a square matrix A are integers and |A|= + or - 1, show that all entries of A^-1 are integers.

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- March 27th 2007, 08:20 AMbuckaroobillProof about square matrix
I found this example in a book of practice problems and if someone could explain this to me, I would be really grateful:

If all entries of a square matrix A are integers and |A|= + or - 1, show that all entries of A^-1 are integers. - March 27th 2007, 09:32 AMfrenzy
- March 27th 2007, 09:50 AMbuckaroobill
Thanks! So can I just say for the proof that...

If |A|= +-1, then A^-1 will be comprised of all integers because A is a matrix of cofactor determinants (which are all integers). A determinant of an integer matrix is just an integer because it is the sum of integer products. - March 27th 2007, 02:01 PMfrenzy
yes