Need some major help. Please let me know if I am headed in the right direction or If I am completely off.

1. What must be true about x, y, z and w if AB = BA for the matrices

A = x y
z w

B= 1 1
-1 1


This is what I got so far.

AB=

X y 1 1 .
Z w -1 1

X*1 X*1 y*-1 y*1 = x-y x+y
Z*1 Z*1 + w*-1 w*1 z-w z+w



BA=
1 1 x y
-1 1 z w

1*x 1*y + 1*z 1*w = x+z y+w
-1*x -1*y + 1*z 1*w -x+z -y+w

For one thing,

\begin{bmatrix}x&y\\z&w\end{bmatrix}=\begin{bmatrix}1&0\\0&1\end{bmatrix}