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**[Solved] Calculate the determinant of a 3x3 matrix**

## Homework Statement

Use elementary row operations to calculate the determinant of this 3x3 matrix.

Code:

```
1-a 1 1
1 1-a 1
1 1 1-a
```

## Homework Equations

I think that the problem wants me to reduce this to an upper triangular matrix and multiply the diagonals to find the determinant. Scaling a row scales the determinant. Swapping a pair of rows/columns flips the sign of the determinant.

## The Attempt at a Solution

I know how to calculate the determinant through cofactors, but I don't know how to approach the problem through row reduction.

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