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

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

If A=[1101], prove that A^(n)=[1n01] for all positive integers n.

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

If A=[[1,1],[1,1]] ,prove that A^n=[[2^(n-1),2^(n-1)],[2^(n-1),2^(n-1)]], for all positive integers n.

let A=[[1,01,1]] and I=[[1,00,1]] prove that A^(n)=nA-(n-1)I,n>=1

If prod_(r=1)^(n)[[1,r],[0,1]]=[[1,120],[0,1]] then n = ?

If A=[ab01], prove that A^(n)=[a^(n)b((a^(n)-1)/(a-1))01] for every positive integer n.

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

Prove that i^(n)+i^(n+1)+i^(n+2)+i^(n+3)=0 for all n inN