A= [ array cc x+y & y x & x-y array ], B= [ array l 3 -2 array ] and C= [ array l 4 -2 array ] . If A B=C , then what is A ^2 equal to?

Step-by-step solution

aligned & A= [ array cc x+y & y x & x-y array ], B= [ array c 3 -2 array ], c= [ array c 4 -2 array ] & A B=C & [ array c 3 x+3 y-2 y 3 x-2 x+2 y array ]= [ array c 4 -2 array ] & 3 x+y=4 ; x+2 y=-2 aligned Solving these equations, gathered 3 x+y=4 3 x+6 y=-6 (-)(-)(+) -5 y=10 gathered aligned & y=-2 & So, 3 x-2=4 3 x=6 x=2 & A= [ array cc 0 & -2 2 & 4 array ], A^2= [ array cc 0 & -2 2 & 4 array ] [ array cc 0 & -2 2 & 4 array ] & = [ array cc -4 & -8 8 & 12 array ] aligned