Answer the following questions.If `A=[[2,-1],[-1,2]]`show that`A^ 2-4A+3I=0`

Answer the following questions. If A=[[3,-5],[-4,2]] ,show that A^2-5A-14I=0

Answer the following questions. If A=[[2,-1],[3,-2]] ,find A^3

Answer the following questions.If A=[[4,-1,-4],[3,0,-4],[3,-1,-3]] ,show that A^2=I

Answer the following questions.If A=[[2,-2,-4],[-1,3,4],[1,-2,-3]] , show that A^2=A

Answer the following questions.If A=[[3,-4],[1,-1]] ,prove that A^n=[[1+2n,-4n],[n,1-2n]] for all n in N

Answer the following questions.If A=[[0,1],[1,0]],B=[[0,-1],[1,0]] ,show that (A+B).(A-B)!=A^2-B^2

If A = [[3,1],[-1,2]] then show that: A^2-5A+7I = 0 .

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

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.

Answer the following questions.If A=[[1,2,3],[2,4,6],[1,2,3]] and B=[[1,-1,1],[-3,2,-1],[-2,1,0]] ,show that AB and BA are both singular matrices.