1. ## Matrices

Explain why the determinant of a matrix with integer entries must be an integer.

2. ## Re: Matrices

Originally Posted by Civy71
Explain why the determinant of a matrix with integer entries must be an integer.
Is this a serious question?
How are determinants calculated? What do operations on integers yield?

3. ## Re: Matrices

I came up with the following answer: Since the product of integers is always an integer, each elementary product is an integer and so the sum of the elementary products is an integer. Is that the best way to explain it? Thanks.

4. ## Re: Matrices

Originally Posted by Civy71
I came up with the following answer: Since the product of integers is always an integer, each elementary product is an integer and so the sum of the elementary products is an integer. Is that the best way to explain it? Thanks.
yes, the only operations that are involved in determinant calculation are addition, multiplication.