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

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

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=[[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=[[2,1],[0,3]],B=[[1,2],[3,-2]] ,verify that |AB|=|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

Answer the following questions. If A=[[3,-5],[-4,2]] ,show that A^2-5A-14I=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,-2,-4],[-1,3,4],[1,-2,-3]] , show that A^2=A

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.