If `A=[[1,0],[1,1]]` then `A^(n)` is equal to

If A=[[1,10,1]], then A^(n) is equal to

If A=|[1,a],[0,1]| , then A^(n) is equal to

If A=[[i,0],[0,i]];i=sqrt(-1), then A^(n) is equal to

If the product of n matrices [[1,10,1]][[1,20,1]][[1,30,1]]......[[1,n0,1]] is equal to the matrix ,[[1,3780,1]] then the value of n is equal to

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

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)/(3),0,0],[0,(1)/(4),0],[0,0,(1)/(5)]] then sum_(n=1)^(oo)A^(n) is equal to

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),(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