SOLUTION: 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

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Question 31028: 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
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
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
------------------------------------------------
AB=
X-Y,X+Y
Z-W,Z+W

BA=
X+Z,Y+W
-X+Z,-Y+W

AB=BA....HENCE
X-Y=X+Z............OR Y=-Z
X+Y=Y+W............OR X=W
Z-W=-X+Z........OR X=W
Z+W=-Y+W.........OR Y=-Z
HENCE WE SHOULD HAVE......X=W AND Y=-Z