If `A=[[8,4],[10,5]],B=[[5,-4],[10,-8]]`show that `(A+B)^2=A^2+AB+B^2`

If A=[[1,2],[3,5]],B=[[0,4],[2,-1]] show that AB!=BA but |AB|=|A|.|B|

If A=[[3,4],[-4,3]] and B=[[2,1],[-1,2]] show that (A+B) . (A-B)=A^2-B^2

If A=[[4,3,2],[-1,2,0]],B=[[1,2],[-1,0],[1,-2]] show that matrix AB is non singular.

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

If A=[[2,-3],[5,-4],[-6,1]],B=[[2,1],[4,-1],[-3,3]] and C=[[1,2],[-1,4],[-2,3]] ,show that (A+B)^T=A^T+B^T

If A=[[2,-3],[5,-4],[-6,1]],B=[[-1,2],[2,2],[0,3]] and C=[[4,3],[-1,4],[-2,1]] show that: A+B=B+A

If A=[[2,-1,3],[4,0,5]] and B=[[-3,-2,-1],[-5,5,1]] .Verify that (A+B)'=A'+B'

If A=[[2,-1,3],[4,0,5]] and B=[[-3,-2,-1],[-5,5,1]] .Verify that (A-B)'=A'-B'

Answer the following questions. If A=[[1,-1,0],[2,3,4],[0,1,2]] and B=[[2,2,-4],[-4,2,-4],[2,-1,5]] ,show that BA=6I