Matrices

To find the value of the determinant , we will calculate it step-by-step using the formula for a 3x3 determinant. The determinant of a 3x3 matrix is given by:

Here, we apply this formula to our matrix:

Simplifying each term, we find:

Substituting back, we have:

This simplifies to:

Continuing simplification:

Recognizing differences and rearranging terms, we find:

The determinant is:

Thus, the correct answer is (a-b)(b-c)(c-a).