If `A=[[3,-4],[1,-1]]` then `A^(n)=`

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

Prove by method of induction: P(n) = [[3,-4],[1,-1]]^n = [[2n+1, -4n],[n, -2n+1]]

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