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 May 6th, 2009, 04:59 AM #1 Newbie   Joined: Apr 2009 Posts: 28 Thanks: 0 Values of the determinant Let P be a square matrix of order greater than 1 and with positive integer entries. Suppose that P^(?1) exists and has integer entries. Then the set of all possible values of the determinant of P is (A) {1}. (B) {?1, 1}. (C) all non-zero integers. (D) all positive integers. I guess it would be (C). Please verify.....Thanks.
 May 6th, 2009, 05:36 PM #2 Senior Member   Joined: Nov 2007 Posts: 258 Thanks: 0 Re: Values of the determinant $det {P^{-1}}= 1/ det {P}$ Since both $det P$ and $det {P^{-1}}$ are integers, the only possible values are {1,-1}.

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