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

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

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

If [[1,1],[0,1]] , prove that A^n=[[1,n],[0,1]] for all positive integers ndot

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.

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

Let A=[(1,1,1),(0,1,1),(0,0,1)] prove that by induction that A^n=[(1,n,n(n+1)/2),(0,1,n),(0,0,1)] for all n in N .

If x=sum_(n=0)^oo a^n, y=sum_(n=0)^oo b^n where |a|<1,|b|<1 then prove that sum_(n=0)^oo (ab)^n=(xy)/(x+y-1)