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

Let A be a square matrix all of whose entries are integers. Then which one of the following is true?

A

If det `Ane ± 1`, then `A^(–1)` exists and all its entries are non-integers

B

If det `A = ± 1`, then `A^(–1)` exists and all its entries are integers

C

If det `A = ± 1`, then `A^(–1)` need not exist

D

If det `A=pm1`, then `A^(-1)` exists but all its entries are not necessarily integers

Text Solution

Verified by Experts

The correct Answer is:
B
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