0!=---

Choose the correct answer in questions 17 to 19: If x, y, z are nonzero real numbers then the inverse of metrix A=[{:(x,0,0),(0,y,0),(0,0,z):}] is : (a) [{:(x^(-1),0,0),(0,y^(1),0),(0,0,z^(1)):}] (b) xyz[{:(x^(-1),0,0),(0,y^(1),0),(0,0,z^(1)):}] ( c) 1/(xyz)[{:(x,0,0),(0,y,0),(0,0,z):}] (d) 1/(xyz)[{:(1,0,0),(0,1,0),(0,0,1):}]

let P_(1)=[(1,0,0),(0,1,0),(0,0,1)],P_(2)=[(1,0,0),(0,0,1),(0,1,0)],P_(3)=[(0,1,0),(1,0,0),(0,0,1)],P_(4)=[(0,1,0),(0,0,1),(1,0,0)],P_(5)=[(0,0,1),(1,0,0),(0,1,0)],P_(6)=[(0,0,1),(0,1,0),(1,0,0)] and X=sum_(k=1)^(6) P_(k)[(2,1,3),(1,0,2),(3,2,1)]P_(k)^(T) Where P_(k)^(T) is transpose of matrix P_(k) . Then which of the following options is/are correct?