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It seems like you're working on calculating the determinant of a 3x3 matrix, and the result you obtained is \(-720\), but the system has marked this as incorrect.

Let's verify the calculation of the determinant for the matrix:

\[
\begin{vmatrix}
-6 & -3 & 6 \\
8 & -8 & -7 \\
-7 & -8 & -5
\end{vmatrix}
\]

### Step-by-step calculation using cofactor expansion:
We will expand along the first row \((-6, -3, 6)\):

\[
\text{Determinant} = -6 \cdot \begin{vmatrix} -8 & -7 \\ -8 & -5 \end{vmatrix}
- (-3) \cdot \begin{vmatrix} 8 & -7 \\ -7 & -5 \end{vmatrix}
+ 6 \cdot \begin{vmatrix} 8 & -8 \\ -7 & -8 \end{vmatrix}
\]

Now, let's compute each 2x2 determinant:

1. \(\begin{vmatrix} -8 & -7 \\ -8 & -5 \end{vmatrix} = (-8)(-5) - (-7)(-8) = 40 - 56 = -16\)
   
2. \(\begin{vmatrix} 8 & -7 \\ -7 & -5 \end{vmatrix} = (8)(-5) - (-7)(-7) = -40 - 49 = -89\)
   
3. \(\begin{vmatrix} 8 & -8 \\ -7 & -8 \end{vmatrix} = (8)(-8) - (-8)(-7) = -64 - 56 = -120\)

Substitute these values back into the determinant expansion:

\[
\text{Determinant} = -6(-16) + 3(-89) + 6(-120)
\]
\[
= 96 - 267 - 720 = -891
\]

### Correct Determinant: \(-891\)

So, the correct determinant is \(-891\), not \(-720\). It looks like that’s the mistake in your previous calculation.

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Would you like to go over any step in more detail or have any other questions? 

Here are some related questions you might want to explore:
1. What is the cofactor expansion method for a 3x3 matrix?
2. How do you calculate the determinant of a 2x2 matrix?
3. Why does the determinant of a matrix tell us whether the matrix is invertible?
4. Can the determinant be calculated using row reduction methods?
5. How does changing one row or column affect the determinant of a matrix?

**Tip:** Always double-check your calculations for each minor determinant to avoid errors in your final result.

Calculate the 3x3 determinant: |-6 -3 6| | 8 -8 -7| |-7 -8 -5|.

This detailed guide explains how to calculate the determinant of a 3x3 matrix using cofactor expansion. Solve the determinant of the matrix |-6 -3 6| | 8 -8 -7| |-7 -8 -5| and understand each step of the process. The correct result is -891. Suitable for Grades 10-12 and linear algebra learners.

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