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=[[2,-1],[3,-2]] ,find A^3

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],[-1,2]] show that A^ 2-4A+3I=0

Answer the following questions.If A=[[2,-4],[3,-2],[0,1]],B=[[1,-1,2],[-2,1,0]] ,show that (AB)^T=B^TA^T

Answer the following questions. If A=[[2,1,-3],[0,2,6]],B=[[1,0,-2],[3,-1,4]] ,find AB^T and A^TB

Answer the following questions. If A=[[2,1],[0,3]],B=[[1,2],[3,-2]] ,verify that |AB|=|A||B|

Answer the following questions.If A=[[2,-3],[3,-2],[-1,4]],B=[[-3,4,1],[2,-1,-3]] verify (3A-5B^T)^T=3A^T-5B

Answer the following questions.If A=[[2,-3],[3,-2],[-1,4]],B=[[-3,4,1],[2,-1,-3]] verify (A+2B^T)^T=A^T+2B

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