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, 0, 0], [0,-1, 0], [0, 0,-1]] , find A^3 .

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=[[1,2,3],[0,1,0],[1,1,0]] and B=[[-1,1,0],[0,-1,1],[2,3,4]] show that AB!=BA

If A=[[1, 0 ,2 ],[0 ,2 ,1],[2, 0 ,3]] , prove that A^3-6A^2+7A+2I=0

Show that [[1,1],[0,1]]^2 = [[1,3],[0,1]]

If [1\ -1\ \ x][[0, 1,-1 ],[2 ,1 ,3],[ 1, 1, 1]][[0 ],[1],[ 1]]=0 , find xdot

If A=|[3, 0,-1], [2, 3 ,0], [0, 4, 1]| , then find |a d j\ (a d j\ A)| .