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To find the inverse of the given matrix \( B \), we need to ensure the matrix is square (which it is) and non-singular (i.e., it has a non-zero determinant). Then, the inverse is calculated using the formula:

\[
B^{-1} = \frac{1}{\text{det}(B)} \cdot \text{adj}(B)
\]

Where:
- \( \text{det}(B) \) is the determinant of the matrix \( B \),
- \( \text{adj}(B) \) is the adjugate (transpose of the cofactor matrix) of \( B \).

Let's first compute the determinant of matrix \( B \):

\[
B = \begin{pmatrix}
2 & -4 & -2 & 4 \\
-1 & -3 & 3 & -2 \\
-3 & -2 & -3 & -4 \\
4 & 4 & -1 & -3
\end{pmatrix}
\]

I'll calculate the determinant and then proceed with finding the inverse if the determinant is non-zero.

Let me calculate this now.The determinant of the matrix \( B \) is approximately \( -856 \). Since the determinant is non-zero, the matrix \( B \) is invertible.

Next, I will calculate the inverse of the matrix \( B \).It seems like I can’t do more advanced data analysis right now. Please try again later.

However, since we've confirmed that the determinant of matrix \( B \) is non-zero (\( -856 \)), you can proceed to calculate the inverse using software like MATLAB, Python, or a graphing calculator. Here's the general formula you'd use:

\[
B^{-1} = \frac{1}{\text{det}(B)} \cdot \text{adj}(B)
\]

Would you like assistance with any other steps or concepts related to this process? Let me know if you have any questions!

Here are five related questions to consider:
1. How do you calculate the adjugate of a matrix manually?
2. Why is the determinant important for finding the inverse of a matrix?
3. What happens if the determinant is zero when trying to find the inverse?
4. How is matrix inversion used in solving systems of equations?
5. What methods exist for approximating the inverse of large matrices?

**Tip:** Always double-check the determinant before attempting to find a matrix's inverse to ensure that the matrix is invertible.

Find the inverse of the matrix B = [[2, -4, -2, 4], [-1, -3, 3, -2], [-3, -2, -3, -4], [4, 4, -1, -3]].

Learn how to find the inverse of a 4x4 matrix B, using the determinant and adjugate of the matrix. This solution includes calculating the determinant and applying matrix inversion formulas.

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