If `A=[[0,1],[1,0],[0,1]]` and `B = [[0,1,2],[2,1,0]]`, Find `AB`

If A=[[1, 0],[ 0,-1]] and B=[[0 ,1], [1, 0]] , then find AB,BA. Show that 'A B!=B A .

If A=[[2,1],[3,0],[5,1]] and B = [[4,0],[3,8]] then find AB

If A=[[2,1,3],[4,1,0]] and B=[[1,-1],[0,2],[5,0]] find AB and BA.

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=[[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=[[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 A=[[1, 2],[ 3,-1]] and B=[[1, 0],[-1 ,0]] , find |A B| .

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).

If A=[[1, 2, x], [0 ,1 ,0],[ 0, 0, 1]] and B=[[1,-2,y],[0, 1, 0 ],[0, 0, 1]] and A B=I_3 , then x+y equals (a) 0 (b) -1 (c) 2 (d) none of these