Which of the following is (are) NOT the square of a `3xx3` matrix with real entries? (a)`[[1, 0, 0],[ 0, 1, 0],[ 0, 0,-1]]` (b) `[[-1, 0, 0] ,[0,-1, 0],[ 0, 0, -1]]` (c)`[[1, 0, 0],[ 0, 1, 0],[ 0, 0, 1]]` (d) `[[1, 0, 0],[ 0,-1, 0],[ 0, 0,-1]]`

If A^(-1)=[[1,-1, 2],[0, 3,1],[ 0 ,0,-1/3]] , then |A|=-1 b. adj A=[[-1, 1 ,2],[ 0,-3,-1],[ 0, 0, 1/3]] c. A=[[1, 1/3, 7 ],[0, 1/3, 1],[0 ,0,-3]] d. A =[[1,-1/3,-7],[ 0,-3, 0],[ 0, 0, 1]]

The inverse of [[0, 0, 1], [0, 1, 0], [1, 0, 0]] is

If A=[[0, 1, 0], [1, 0, 0], [0, 0, 1]] , then A^(-1)=

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

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]]

Q7Which of the following is a symmetric as well as skew-symmetric matrix : (a) [[1,2],[1,0]] (b) [[0,0],[0,0]] (c) [[1,0],[0,1]]

If A=[[1,0,0],[0,1,0],[a,b,-1]] and A=A^(-1) then a+b=?

If A = [ [ 0 , 1 ] , [ 0 , 1 ] ] ,then A^2 is equal to ( a ) [ [ 0 , 1 ] , [ 1 , 0 ] ] ( b ) [ [ 1 , 0 ] , [ 1 , 0 ] ] ( c ) [ [ 0 , 1 ] , [ 0 , 1 ] ] ( d ) [ [ 1 , 0 ] , [ 0 , 1 ] ]

Which one of the following is correct in respect of the matrix ? [{:(0,0,-1),(0,-1,0),(-1,0,0):}] ?

Volume of tetrahedron with vertices at (0, 0, 0), (1, 0, 0), (0, 1, 0), (0, 0, 1) is