If the matrix `A=[[2,0,2] , [0,2,0] , [2,0,02]]` then `A^n=[[a,0,0] , [0,a,0] , [b,0,a]], n in N` where

If the matric A=((2,0,0),(0,2,0),(2,0,2)) , then A^(n)=((a,0,0),(0,a,0),(b,0,a)), n in N where

The matrix [[0,2,-4],[-2,0,-6],[4,6,0]] is

A =[[0,0],[0,0]] and B=[[1,0],[0,2]]

If A=[(0,2),(0,3)] and B =[(2,5),(0,0)] then AB =[(0,0),(0,0)]

(0,2) . (0,2) = (0,4)

Verify that the matrix equation A^2 - 4a +3I =0 is satisfied by the matrix A = [[2,-1],[-1,2]] , where I = [[1,0],[0,1]] and 0= [[0,0],[0,0]] ,

If M = [[0,2],[5,0]] and N = [[0,5],[2,0]]then M^(2011) is,

If the product of n matrices [[1,n][0, 1] [[1, 2],[ 0 , 1]] [[1 , 3],[ 0, 1]][[1, n],[ 0 , 1]] is equal to the matrix [[1, 378], [0 , 1]] then the value of n is equal to

Verify that the matrix equation A^(2)-4A+3I = 0 is satisfied by the matrix A={:[(2,-1),(-1,2)]," where " I={:[(1,0),(0,1)]and 0={:[(0,0),(0,0)]. Hence obtain A^(-1).