Let  A=xyzyzxzxy, where x,y  andz  are real numbers such that x+y+z>0 and xyz=2 . If A2=I3, then the value of x3+y3+z3 is_________.

Given A2=xyzyzxzxyxyzyzxzxy=100010001it gives  x2+y2+z2=1;  xy+yz+zx=0Consider the determinantsA2=I=1⇒A=-1A=3xyz−x3−y3−z3                                               =−x+y+zx2+y2+z2−xy−yz−zx6−x3+y3+z3=−1x3+y3+z3=7 Therefore, x3+y3+z3=7