`if A=[{:(3,-4),(1,-1):}] ,` then prove that `a^(n) =[{:(1+2n,-4n),(n,1-2n):}],` where n is any posttive interger.

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+2n,-4n],[n,1-2n]] , where n is any positive integer.

if A=[{:(3,-4),(1m,-1):}], then show that A^(n)=[{:(1+2n,-4n),(n,1-2n):}] is true for all natural values of n.

Prove that (1+i)^n+(1-i)^n=2^((n+2)/2).cos((npi)/4) , where n is a positive integer.

Prove that (1+i)^n+(1-i)^n=2^((n+2)/2).cos((npi)/4) , where n is a positive integer.

Prove that n! (n+2) = n! +(n+1)! .

Prove that: n !(n+2)=n !+(n+1)!

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

Show that one and only one out of n,( n+2) and ( n +4) is divisble by 3, where n is any positive interger.

Prove that: \ ^(2n)C_n=(2^n[1. 3. 5 (2n-1)])/(n !)