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

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

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]]

The value of x so that [[1,x,1]][[1,3,2] , [0,5,1] , [0,3,2]][[1], [1], [x]]=0 is

Evaluate the following : [[1,-1],[0,2],[2,3]]([[1,0,2],[2,0,1]]-[[0,1,3],[1,0,2]])

If A=[[1, 0],[ 0, 1]] , B=[[1,0],[0,-1]] and C=[[0, 1],[ 1, 0]] , then show that A^2=B^2=C^2=I_2 .

If A=[[3,1],[-1,2]], I=[[1,0],[0,1]] and O=[[0,0],[0,0]] , show that A^2-5A+7I=0 . Hence find A^(-1) .

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= [[2,4,-1],[-1,0,2]], B=[[3,4],[-1,2],[2,1]] , Show that (AB)'=B'A' .

The matrix X in the equation AX=B, such that A= [(1,3),(0,1)] and B= [(1,-1),(0,1)] is given by (A) [(1,0),(-3,1)] (B) [(1,-4),0,1)] (C) [(1,-3),(0,1)] (D) [(0,-1),(-3,1)]

If A=[[1,2,3],[2,0,-2]],B=[[1,1,-1],[2,0,3],[3,-1,2]] and C=[[1,3],[0,2],[-1,4]] find A(BC).