Let A= [ array cc x+y & y 2 x & x-y array ], B= [ array c 2 -1 array ] and C= [ array l 3 2 array ] If A B=C , then what is A^2 equal to?

Step-by-step solution

aligned & A = [ array cc x + y & y 2 x & x - y array ] & B = [ array c 2 -1 array ] and C = [ array l 3 2 array ] aligned Here AB = C aligned & [ array cc x+y & y 2 x & x-y array ] [ array c 2 -1 array ]= [ array l 3 2 array ] & [ array cc 2(x+y) & -y 4 x & -x+y array ]= [ array l 3 2 array ] & 2 x+y=3 ...(i) & 3 x+y=2...(ii) aligned From equations (i) and (ii), we get x=-1 and y=5 aligned & A= [ array cc 4 & 5 -2 & -6 array ] & Now, A^2= [ array cc 4 & 5 -2 & -6 array ] [ array cc 4 & 5 -2 & -6 array ] & = [ array