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]]`

If A=[[1, -1, 2], [3, 0, -2], [1, 0, 3]] , then (adjA)A=

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=[[-3,1,2],[0,0,1],[-3,5,0]] ,then 8|A|

If A=|[1,0,1],[0,1,2],[0,0,4]| then |3A|

Show that(i) [[5,-1],[ 6 ,7]][[2, 1],[ 3 ,4]]!=[[2, 1],[ 3, 4]][[5,-1],[ 6, 7]] (ii) [[1, 2, 3],[ 0, 1, 0],[ 1, 1, 0]][[-1, 1, 0],[ 0,-1, 1],[ 2, 3, 4]]!=[[-1, 1, 0],[ 0,-1, 1],[ 2, 3, 4]][[1 ,2 ,3],[ 0, 1, 0],[ 1, 1, 0]]

If A=[[0,0,1],[0,1,0],[1,0,0]],B=[[0,5,7],[0,0,6],[0,0,0]] and C=[[-1,3,5],[1,-3,-5],[-1,3,5]] , show that C^2=C

If [[2, 1],[ 3, 2]]A[[-3 ,2],[ 5,-3]]=[[1 ,0],[ 0, 1]], then "A= (A) [[1, 1],[ 1 ,0]] (B) [[1, 1],[ 0, 1]] (C) [[1 ,0],[ 1 ,1]] (D) -[[1, 1],[ 1, 0]]

If A=[[0,0,1],[0,1,0],[1,0,0]],B=[[0,5,7],[0,0,6],[0,0,0]] and C=[[-1,3,5],[1,-3,-5],[-1,3,5]] , show that A^2=I

If A=[[0,0,1],[0,1,0],[1,0,0]],B=[[0,5,7],[0,0,6],[0,0,0]] and C=[[-1,3,5],[1,-3,-5],[-1,3,5]] , show that B^4=O

If A=[[-2, 0, 0], [-2, -1, 3]], B=[[0, 1], [2, 3], [1, -1]] , then