Let A be a square matrix all of whose entries are integers. Then which one of the following is true?(a) If det A = ± 1, then A⁻¹ exists but all its entries are not necessarily integers(b) If det A ≠ ± 1, then A⁻¹ exists and all its entries are non integers(c) If det A = ± 1, then A⁻¹ exists but all its entries are integers(d) If det A = ± 1, then A⁻¹ need not exists
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Let A be a square matrix all of whose entries are integers. Then which one of the following is true?(a) If det A = ± 1, then A⁻¹ exists but all its entries are not necessarily integers(b) If det A ≠ ± 1, then A⁻¹ exists and all its entries are non integers(c) If det A = ± 1, then A⁻¹ exists but all its entries are integers(d) If det A = ± 1, then A⁻¹ need not exists
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