[" (10) 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=[[3, -4],[ 1, (-1)]] , then prove that A^n=[[1+2 n, -4 n ],[n , 1-2n]] where n is any positive integer.

If A,=[[3,-41,1]], then prove that A^(n),=[[1+2n,-4n][2n], where n is any positive integer.

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

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

Prove that 2^(n)>1+n sqrt(2^(n-1)),AA n>2 where n is a positive integer.

If A=[(3,-4),(1,-1)] , prove by induction that A_n=[(1+2n,-4n),(n,1-2n)],n in N

Prove the following by principle of mathematical induction : (a) If A=[{:(11,-25),(4,-9):}] , then A^(n)=[{:(1+10n,-25n),(4n,1-10n):}] where n is a positive integer .

Answer the following questions.If A=[[3,-4],[1,-1]] ,prove that A^n=[[1+2n,-4n],[n,1-2n]] for all n in N

IF A=[{:(3,-4),(1,-1):}] then show that A^n=[{:(1+2n,-4n),(n,1-2n):}] , for any integer n ge1 .