If the entries of A and A 1 are all integers, how do you know that both determinants are

Chapter 4, Problem 4.5

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QUESTION:

If the entries of A and A 1 are all integers, how do you know that both determinants are 1 or 1? Hint: What is detA times detA 1 ?

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QUESTION:

If the entries of A and A 1 are all integers, how do you know that both determinants are 1 or 1? Hint: What is detA times detA 1 ?

ANSWER:

Step 1 of 2

It is given that the entries of   and  are all integers.

To prove that both determinants are  or .

 The inverse of a matrix is determined as,

.

And,

.

 

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