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

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.

If A=[[3,-4],[1,-1]] , then prove that A^n=[[1+2n,-4n],[n,1-2n]] , where n is any positive integer.

If a is a non-zero real or complex number. Use the principle of mathematical induction to prove that: IfA=[[a,1],[ 0,a]],t h e nA^n=[[a^n,n a^(n-1)],[0,a^n]] for every positive integer n.

Prove the following by principle of mathematical induction If A=[[3,-4] , [1,-1]] , then A^n=[[1+2n, -4n] , [n, 1-2n]] for every positive integer n

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 .

Given that u_(n+1)=3u_n-2u_(n-1), and u_0=2 ,u_(1)=3 , then prove that u_n=2^(n)+1 for all positive integer of n

If a is a non-zero real or complex number. Use the principle of mathematical induction to prove that: If A=[a1 0a] , then A^n=[a^nn a^(n-1)0a^n] for every positive integer ndot

Using mathematical induction prove that d/(dx)(x^n)=n x^(n-1) for all positive integers n.

Using binomial theorem, prove that 5^(4n)+52n-1 is divisible by 676 for all positive integers n.

If A= [(3 , -4), (1 , -1) ] , then prove that A^n=[(1+2n , -4n), (n , 1-2n) ] , where n is any positive integer.