If A=`[[-1,3,5],[1,-3,-5],[-1,3,5]]`,show that `A^2`=A

If A=[[0,0,1],[0,1,0],[1,0,0]],B=[[0,5,7],[0,0,6],[0,0,0]] and C=[[-1,3,5],[1,-3,-5],[-1,3,5]] , show that A^2=I

If A=[[0,0,1],[0,1,0],[1,0,0]],B=[[0,5,7],[0,0,6],[0,0,0]] and C=[[-1,3,5],[1,-3,-5],[-1,3,5]] , show that C^2=C

If A=[(2 ,-3, -5), (-1, 4, 5),( 1, -3 ,-4)] and B=[(-1, 3, 5), (1,-3, -5) , (-1, 3, 5)] , show that A B=B A=O_3xx3 .

If A=[[-1,2],[3,4]] and B=[[2,-3],[5,1]] show that AB!=BA

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

If A=[[2,4],[-5,-1]] show that: |3A|=9|A|

If A=|[2, 3], [5,-2]| , show that A^(-1)=1/(19)Adot

If A = [[2,3],[-1,5]] , B = [[3,-1],[4,7]] and C = [[5,-1],[0,3]], show that A(B +C)=AB+AC

If A= [{:(,3,-4),(,1,-1)]:} then show that A^(3)=[{:(,7,-12),(,3,-5)]:}

If A=[(3, 1),( 1, 2)] , show that A^2-5A+5I=0 . Hence, find A^(-1) .