If A=`[[1,2,-1],[3,0,2],[4,5,0]] `B=`[[1,0,0],[2,1,0],[0,1,3]]` Find `(AB)^T`

If A=[[1,0,0],[0,1,0],[a,b,-1]] , find A^2

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

If A=[[3, -1, 4], [2, 3, 1]], B=[[1, 3, 4], [2, 1, 0], [-3, 2, 3]] find AB

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

Given A=[[1,2,-3],[5,0,2],[1,-1,1]] and B=[[3,-1,2],[4,2,5],[2,0,3]] , find the matrix C such that A+C=B.

If A=[[1,0,-2],[3,-1,0],[-2,1,1]],B=[[0,5,-4],[-2,1,3],[-1,0,2]] and C=[[1,5,2],[-1,1,0],[0,-1,1]] verify that A(B-C)=(AB-AC)

If A=[[2,1,3],[4,1,0]], B=[[1,-1],[0,2],[5,0]] , verify that (AB)\'=B\'A\'

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

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,-3] , [5,0,2] , [1,-1,1]] and B=[[3,-1,2] , [4,2,5] , [2,0,3]] then find matrix C such that A+2C=B