Scores and Estimated Grade

section 1.3#14

Hello Professor Taylor, I have been stuck on this problem for what seems like weeks and I can't figure it out. First, I multiplied AB and BA to get:
AB= |x^2 x^2-5y|
         |xy    xy-6y |
and
BA= |x^2-5x xy-6x |
         |-5y       -6y     |
I understand why (0,0) is a solution, but every other set of points I try don't work. My thought process in solving this is to set each similar location equal to each other and then solve a system of equations, but then the values i get only work for that one system, not the overall matrix.
Ex:
x^2 = x^2 -5x
x^2 = x(x-5)
x = 0
But, I can't think of any other possible values that might work. Could you help lead me to the right direction? Thank you very much for your time!

*******************
OK, the simple answer is that you multiplied BA incorrectly :

BA = |x   x|  |x  -5|    =   | x*x + x*y    x*(-5) + x*(-6) |   =  | x^2+xy   -11x |
         |0   y|  |y  -6|         | 0*x + y*y    0*(-5) + y*(-6) |       |    y^2       -6y  |

     =  | x^2+xy   -11x |
         |    y^2       -6y  |

This gives me the simultaneous equations

x^2 = x^2 + xy ==> xy = 0 ==> x=0 or y=0
xy = y^2 ==> y^2=0 because xy=0 from line just above hence y=0
xy = -6y ==> trivial from line just above
x^2-5y = -11x ==> x^2+11x = 0 (since y=0) hence x(x+11)=0 hence x=0 or x=-11.
Since we already know that y=0 the solutions are
(0,0) and (-11,0)

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