Let A and B be matrices, and let x and y be vectors such that neither is a scalar multiple of the other satisfying

Ax=y, Ay=x+2y

and

Bx=x+y, By=2y.

Then there exist scalars a, b, c, and d such that

(AB)x=ax+by, (BA)x=cx+dy.

Find a, b, c, and d.

Guest Jul 6, 2021