1.6.2 Fields, Groups, Rings

Problem: Find the matrix centralizer \( A=\left(\begin{array}{ll}3 & -4 \\ 1 & -2\end{array}\right) \) in \( G L(2, R) \), where \( G L(n, F) \) is a group of non-degenerate matrices of size \( n \times n \) over the field \( F \), with the operation of matrix multiplication.