If `A = [(1,1),(0,1)]` then show that `A^n = [(1,n),(0,1)]`

If A=[{:(1,1),(0,1):}] , prove that A=[{:(1,n),(0,1):}] for all n inN.

If A=[(1,2),(0,1)], then A^n= (A) [(1,2n),(0,1)] (B) [(2,n),(0,1)] (C) [(1,2n),(0,-1)] (D) [(1,n),(0,1)]

If A= [(1,0),(1,1)] then (A) A^-n=[(1,0),(-n,1)] , n epsilon N (B) lim_(n rarr 00)1/n^2 A^-n = [(0,0),(0,0)] (C) lim_(nrarroo)1/n A^-n = [(0,0),(-1,0)] (D) none of these

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

If [{:(1, 1), (0,1):}]*[{:(1, 2), (0,1):}]*[{:(1, 3), (0,1):}]cdotcdotcdot[{:(1, n-1), (0,1):}] = [{:(1, 78), (0,1):}] , then the inverse of [{:(1, n), (0,1):}] is

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

If A=[(1,a),(0, 1)] , then A^n (where n in N) equals [(1,n a),(0, 1)] (b) [(1,n^2a),(0, 1)] (c) [(1,n a),(0 ,0)] (d) [(n,n a),(0,n)]

if the product of n matrices [(1,1),(0,1)][(1,2),(0,1)][(1,3),(0,1)]…[(1,n),(0,1)] is equal to the matrix [(1,378),(0,1)] the value of n is equal to