if `A=[[1,-2,2],[0,1,-1],[0,0,1]]` and `B=[[1,2,0],[2,3,-1],[0,-1,-2]]` then show that `(A'B)A` is a diagonal matrix.

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

Answer the following questions.If A=[[1,2],[3,2],[-1,0]] and B=[[,1,3,2],[4,-1,-3]] ,show that AB is singular matrix.

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=[[0,1],[1,0],[0,1]] and B=[[0,1,2],[2,1,0]], find AB

If A={:[(1,-1,0),(-1,2,1),(0,1,1)]and B ={:[(1,1,-1),(0,1,-1),(0,0,1)] show that B^(T)AB is a diagonal matrix, where B^(T) is the transpose of B.

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=[[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

Let A=[[2,1,3],[4,1,0]] and B=[[1,-1],[0,2],[5,0]] Show that (AB)^T=B^TA^T

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