If `P=[(x,0, 0),( 0,y,0 ),(0, 0,z)]` and `Q=[(a,0 ,0 ),(0,b,0 ),(0, 0,c)]` , prove that `P Q=[(x a,0 ,0 ),(0,y b,0),( 0 ,0,z c)]=Q P`

If A=[(a, 0,0),(0,b,0),(0,0,c)] and a,b,c are non zero real numbers, then A^-1 is (A) 1/(abc) [(1,0,0),(0,1,0),(0,0,1)] (B) 1/(abc) [(a,0,0),(0,b,0),(0,c,0)] (C) 1/(abc) [(a^-1,0,0),(0,b^-1,0),(0,c^-1,1)] (D) [(a^-1,0,0),(0,b^-1,0),(0,0,c^-1)]

If x ,\ y ,\ z are non-zero real numbers, then the inverse of the matrix 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) x y z[[x^(-1),0 ,0],[ 0,y^(-1),0],[ 0, 0,z^(-1)]] (c) 1/(x y z)[[x,0, 0],[ 0,y,0],[ 0, 0,z]] (d) 1/(x y z)[[1, 0, 0],[ 0 ,1, 0],[ 0, 0, 1]]

Point P(p ,0),Q(q ,0),R(0, p),S(0,q) from.

If x, y, z are non-zero real numbers, then the inverse of matrix 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]]

If [(1 ,0, 0) ,(0 ,1, 0),( 0 ,0 ,1)][(x),( y),( z)]=[(1),(-1),( 0)] , find x ,\ y\ a n d\ z .

If [(1,0,0),(0, 0, 1),(0,1,0)][(x),(y),(z)]=[(2),(-1),(3)] , find x ,\ y ,\ z .

If [(1, 0 ,0 ),(0,y,0),( 0, 0, 1)][(x),(-1),(z)]=[(1),( 0),( 1)] , find x ,\ y\ a n d\ z .

Prove that: |[0,a,-b],[-a,0,-c],[ b, c,0]|=0 .

If [(1,0,0 ), (0,-1,0), (0,0, -1)][(x),(y),( z)]=[(1),(0),(1)] , find x ,\ y\ a n d\ z .

If P(0, 1, 2), Q(4, -2, 1) and R(0, 0, 0) are three points, then anglePRQ is