" 2."(i)|[1,0,0],[0,1,0],[0,0,1]|

Let A=[[1 ,0 ,0], [0 ,1 ,1] ,[0,-2, 4]],I=[[1 ,0 ,0 ],[0, 1, 0], [0, 0, 1]] and A^(-1)=[1/6(A^2+c A+d I)]dot Then value of c and d are

i) Find the rank of the matrix [[1,0,0],[1,0,0],[0,0,1]]

If P=[(i,0,-i),(0,-i,i),(-i,i,0)] and Q=[(-i,i),(0,0),(i,-i)] then PQ is equal to (A) [(-2,2),(1,-1),(1,-1)] (B) [(2,-2),(-1,-1),(-1,1)] (C) [(2,2),(-1,1)] (D) [(1,0,0),(0,1,0),(0,0,1)]

If P=[(i,0,-i),(0,-i,i),(-i,i,0)] and Q=[(-i,i),(0,0),(i,-i)] then PQ is equal to (A) [(-2,2),(1,-1),(1,-1)] (B) [(2,-2),(-1,1),(-1,1)] (C) [(2,2),(-1,1)] (D) [(1,0,0),(0,1,0),(0,0,1)]

The inverse of the matrix [(0,0,1),(0,1,0),(1,0,0)] is (A) [(0,0,1),(0,1,0),(1,0,0)] (B) [(0,0,-1),(0,-1,0),(-1,0,0)] (C) [(1,0,0),(0,1,0),(0,0,1)] (D) [(1/2,0,0),(0,1/2,0),(0,0,1/2)]

The inverse of the matrix [(0,0,1),(0,1,0),(1,0,0)] is (A) [(0,0,1),(0,1,0),(1,0,0)] (B) [(0,0,-1),(0,-1,0),(-1,0,0)] (C) [(1,0,0),(0,1,0),(0,0,1)] (D) [(1/2,0,0),(0,1/2,0),(0,0,1/2)]

Find the rank of B= [[1,0,1,1],[0,0,1,2],[0,1,0,0],[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?

Let A=[(1,0,0),(0,1,1),(0,-2,4)],I=[(1,0,0),(0,1,0),(0,0,1)] and A^-1=[1/6(A^2+cA+dI)] Then value of c and d are (a) (=6,-11) (b) (6,11) (c) (-6,11) (d) (6,-11)