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

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]]

" Let "A" be a "3times3" matrix such that "A[[1,2,3],[0,2,3],[0,1,1]]=[[0,0,1],[1,0,0],[0,1,0]]" .Then "A^(-1)" is "

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

Let A be a 3times3 real matrix such that A([1],[0],[1])=2([1],[0],[1]),A([-1],[0],[1])=4([-1],[0],[1]),A([0],[1],[0])=2([0],[1],[0]) Then,the system (A-3I)([x],[y],[z])=([1],[2],[3]) has :

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]]

8.Find the rank of the matrix [[0,1,-3,-1],[1,0,1,1],[3,1,0,2],[1,1,-2,0]]

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

If A=[[2,1,3],[3,-2,1]] and B=[[1,-1],[0,2],[2,1]] , show that (AB)^'=B^'A^' where A^' is the transpose of A etc.

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)

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