[" 6.If "A=[[a,b],[0,1]]" where "a>=0],[" show that for "n>=0A''=[[a'',(b(a^(n)-1))/(a-1)],[0,1]]]

If A=[[a,b],[0,1]] then prove that A^n=[[a^n,(b(a^n-1))/(a-1)],[0,1]]

If A=[(a,b),(0,1)] , where a ne 1 , then prove that A^(n) =[(a^(n), (b(a^(n)-1))/(a-1)),(0,1)], n in N .

A=[{:(a,b),(0,1):}],ane1 then prove that A^(n)=[{:(a^(n),(b(a^(n)-1))/(a-1)),(0," "1):}], n inN .

If A=[(a, b),(0, 1)] , prove that A^n=[(a^n,b((a^n-1)/(a-1))),(0 ,1)] for every positive integer n .

If A={:[(a,b),(0,1)]:}, prove by mathematical induction that, A^(n)= [{:(,a^(n), (b(a^(n) -1))/(a-1)),(,0,1)]:} for every positive integer n.

If A=[[1,0],[0,1]],B=[[1,0],[0,-1]] and C=[[0,1],[1,0]] then show that A^(2)=B^(2)=C^(2)

If A=[[1,1],[0,1]] , prove that A^n=[[1,n],[0,1]] for all n epsilon N

If A[(-1,0),(0,1)] and B=[(0,1),(1,0)] , show that (A+B)^2 ne A^2+2AB+B^2 .

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

If A=[{:(0,1),(1,1):}] "and" B=[{:(0,-1),(1,0):}] , then show that (A+B)(A-B)neA^(2)-B^(2)