If `A=[1a0 1]` , then `A^n` (where `n in N)` equals `[1n a0 1]` (b) `[1n^2a0 1]` (c) `[1n a0 0]` (d) `[nn a0n]`

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 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=[2-1 3-2] , then A^n= [1 0 0 1] , if n is an even natural number (b) [1 0 0 1] , if n is an odd natural number (c) [-1 0 0 1] , if n in N (d) none of these

IF A = [(1,0),(1,1)] then for all natural numbers n A^n is equal to (A) [(1,0),(1,n)] (B) [(n,0),(1,1)] (C) [(1,0),(n,1)] (D) none of these

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),(1,0)] and n epsilon N then A^n is equal to (A) 2^(n-1)A (B) 2^nA (C) nA (D) none of these

If A=[(1,0,0),(0,1,0),(3,4,-1)] and A^(n)=l , then value of n is equal to

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

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

For positive integer n_1,n_2 the value of the expression (1+i)^(n1) +(1+i^3)^(n1) (1+i^5)^(n2) (1+i^7)^(n_20), where i=sqrt-1, is a real number if and only if (a) n_1=n_2+1 (b) n_1=n_2-1 (c) n_1=n_2 (d) n_1 > 0, n_2 > 0