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Let A be a square matrix all of whose...

Let A be a square matrix all of whose entries are integers. Then which one of the following is true? (1) If `d e t A""=+-1,""t h e n""A^(1)` exists but all its entries are not necessarily integers (2) If `d e t A!=""+-1,""t h e n""A^(1)` exists and all its entries are non-integers (3) If `d e t A""=+-1,""t h e n""A^(1)` exists and all its entries are integers (4) If `d e t A""=+-1,""t h e n""A^(1)` need not exist

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