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 the principle of Mathematical Induction: If A = {:[(3,-4),(1,-1)], then A^n = [(1+2n, -4n),(n,1-2n)] where n in N.

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

Prove the following by using the Principle of mathematical induction AA n in N 2^(n+1)>2n+1

Prove the following by the principle of mathematical induction: 1+2+2^(7)=2^(n+1)-1 for all 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 .

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

Prove the following by the principle of mathematical induction: 1.2+2.3+3.4++n(n+1)=(n(n+1)(n+2))/(3)

Prove the following by the principle of mathematical induction: \ 1. 3+3. 5++(2n-1)(2n+1)=(n(4n^2+6n-1))/3

Prove the following by the principle of mathematical induction: \ 1. 3+3. 5++(2n-1)(2n+1)=(n(4n^2+6n-1))/3

Prove the following by using the principle of mathematical induction for all n in N 4+8 + 12 + …….+4n = 2n (n+1)