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Nonzero real numbers a, b, and c are such that

a²+b+c=1/a
b²+c+a=1/b
c²+a+b=1/c

Find (a-b)(b-c)(c-a)

3 8 7 9 1 6 4 1 5
2 1 6 3 8 7 3 6 6
5 9 4 2 4 5 2 8 7
4 6 7 1 4 9 8 2 3
9 2 1 7 5 2 1 7 8
8 7 3 1 3 9 6 8 3
6 9 4 5 6 7 2 7 1
5 1 8 7 2 3 1 6 3
3 7 2 6 1 2 8 2 5

The above 9*9 matrix was not generated randomly.
There was some principle in its creation - for you to discover.

So what is it??