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 that 2^n >1+nsqrt(2^(n-1)),AAn >2 where n is a positive integer.

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

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