The task involves solving a system of matrix equations by calculating the determinant of matrix $A$, its inverse, and solving $A \cdot X = B$.

Key Steps:

1. Calculate the Determinant of $A$ ($\det(A)$):

   • Use the determinant formula for $4 \times 4$ matrices.

2. Find the Inverse of $A$ ($A^{-1}$):

   • Apply the Gauss-Jordan elimination method or the adjoint formula.

3. Solve $X = A^{-1} \cdot B$:

   • Multiply the inverse matrix $A^{-1}$ with matrix $B$.

Shall I proceed with solving step-by-step or assist with any specific part of the calculation?