The uploaded image contains a matrix equation problem in Russian. The main goal is to solve the matrix equation $A \cdot X = B$, where:

• Matrix $A$ and $B$ are given.
• The determinant of matrix $A$ needs to be computed ($\det A$).
• The inverse matrix $A^{-1}$ must be calculated using the determinant and the Gauss method.
• Finally, the solution to the equation, $X = A^{-1} \cdot B$, must be determined.

Step-by-step outline to solve this:

1. Calculate the determinant of matrix $A$: Use the determinant formula for a 4x4 matrix.

2. Find the inverse of $A$:

   • Use the formula $A^{-1} = \frac{1}{\det A} \text{Adj}(A)$, where $\text{Adj}(A)$ is the adjugate of $A$.
   • Alternatively, use Gaussian elimination to compute $A^{-1}$.

3. Multiply $A^{-1}$ with $B$ to find $X$: Perform matrix multiplication $X = A^{-1} \cdot B$.

Would you like me to proceed step-by-step with the calculations or explain any part in more detail? Let me know if you'd like a numerical solution for these matrices!

Here are five relevant questions to expand your understanding:

1. How do you calculate the determinant of a 4x4 matrix step-by-step?
2. What is the Gaussian elimination method for finding the inverse of a matrix?
3. Why is $\det A \neq 0$ a requirement for finding the inverse of $A$?
4. How do you multiply two matrices to solve $X = A^{-1} \cdot B$?
5. What are the common pitfalls when solving matrix equations manually?

Tip: Always check the determinant value before attempting to calculate the inverse of a matrix. If $\det A = 0$, the matrix is singular, and its inverse does not exist.