If `B=[[0,5,7],[0,0,6],[0,0,0]] `, show that `B^4=O`

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=[[3,1],[-1,2]], I=[[1,0],[0,1]] and O=[[0,0],[0,0]] , show that A^2-5A+7I=0 . Hence find A^(-1) .

If A=[(3, 2, 0),( 1, 4 ,0 ),(0 ,0 ,5)] , show that A^2-7A+10 I=O .

If A=[[0, 6, 7], [-6, 0, 8], [ 7,-8, 0]] , B=[[0, 1, 1],[ 1, 0, 2],[ 1, 2, 0]] , C=[[2], [-2] , [3]] Calculate AC, BC and (A + B)C . Also, verify that (A + B)C = A C + B C

If A=[[2,1,3],[4,1,0]], B=[[1,-1],[0,2],[5,0]] , verify that (AB)\'=B\'A\'

If a matrix A=((3,2,0),(1,4,0),(0,0,5)) show that A^2-7A+10I_(3) = 0 and hence find A^(-1)

If A=[[1, 0],[ 0,-1]] and B=[[0 ,1], [1, 0]] , then find AB,BA. Show that 'A B!=B A .

If A=[[1,4],[0,5],[6,7]] and B=[[2,3,-1],[1,0,-7]] , verify that (AB)\'=B\'A\'

If A ,B ,C have position vectors (2,0,0),(0,1,0),(0,0,2), show that A B C is isosceles.