I would really appreciate any help on this problem.
Let \(\mathbf{A}\) and \(\mathbf{B}\) be matrices, and let \(x\) and \(y \) be vectors such that neither is a scalar multiple of the other satisfying
\(\mathbf{A} \mathbf{x} = \mathbf{y}, \mathbf{A} \mathbf{y} = \mathbf{x} + 2\mathbf{y}\)
and
\(\mathbf{B} \mathbf{x} = \mathbf{x} + \mathbf{y}, \mathbf{B} \mathbf{y} = 2\mathbf{y}.\)
Then there exist scalars \(a, b, c, d\) such that
\(\begin{align*} (\mathbf{A}\mathbf{B})\mathbf{x} = a \mathbf{x} + b\mathbf{y},\\ (\mathbf{B}\mathbf{A})\mathbf{x} = c \mathbf{x} + d\mathbf{y}. \end{align*}\)
Enter \(a, b, c, d\) in that order
Thank for any help in advance