If `A = [[2,3],[-1,5]] , B = [[3,-1],[4,7]] and C = [[5,-1],[0,3]],` show that `A(B +C)=AB+AC`

If A=[[1,2],[5,7]] and B=[[2,0],[ 3,-4]] , show that AB!=BA

If A=[[2,3,4],[-3,0,2]], B=[[3,-4,-5],[1,2,1]] and C=[[5,-1,2],[7,0,3]] , find the matrix X such that 2A+3B=X+C

If =[[2,3],[4,5]],B=[[3,4],[7,2]], C=[[1,0],[0,7]] then verify that (AB)C=A(BC)

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 =[[1,2,3],[-1,0,2],[1,-3,-1]] , B= [[4,5,6],[-1,0,1],[2,1,2]] and C=[[-1,-2,1], [-1,2,3],[-1,-2,2]] verify that A(B+C)=AB+AC .

If A=[[1,4],[0,5],[6,7]] and B=[[2,3,-1],[1,0,-7]] , verify that (AB)\'=B\'A\'

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 A=[[5,1],[6,7]], B=[[2,1],[3,4]],C=[[1,3],[-1,4]] , verify the following (AC)\'=C\'A\'

If A=[[5,1],[6,7]], B=[[2,1],[3,4]],C=[[1,3],[-1,4]] , verify the following (AB)\'=B\'A\'

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