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There appear to be 10 terms in the determinant. A determinant can only have a perfect number of terms. So something has gone wrong with the question.

1: x2 plus 1

2: xy

3: xz

4: xy

5: y2 plus 1

6: yz

7: 1 plus x2 plus y2 plus z2

8: xz

9: yz

10: z2 plus 1

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