[[a,b],[0,1]]," prove that "A^(n)=[[a^(n),b((a^(n-1))/(a-1))],[0,1]]" for every positive integer "n

If A=[ab01], prove that A^(n)=[a^(n)b((a^(n)-1)/(a-1))01] for every positive integer n.

If A=[[a,b],[0,1]] then prove that A^n=[[a^n,(b(a^n-1))/(a-1)],[0,1]]

If A={:[(a,b),(0,1)]:}, prove by mathematical induction that, A^(n)= [{:(,a^(n), (b(a^(n) -1))/(a-1)),(,0,1)]:} for every positive integer n.

If A=[[1,1],[1,1]] ,prove that A^n=[[2^(n-1),2^(n-1)],[2^(n-1),2^(n-1)]], for all positive integers n.

If A=[[1,1],[1,1]] ,prove that A^n=[[2^(n-1),2^(n-1)],[2^(n-1),2^(n-1)]] , for all positive integers n.

If a is a non-zero real or complex number. Use the principle of mathematical induction to prove that: IfA=[[a,1],[ 0,a]],t h e nA^n=[[a^n,n a^(n-1)],[0,a^n]] for every positive integer n.

If a is a non-zero real or complex number.Use the principle of mathematical induction to prove that: If A=[[a,10,a]],then A^(n)=[[a^(n),na^(n-1)0,a^(n)]] for every positive integer n.

If a is a non-zero real or complex number.Use the principle of mathematical induction to prove that: If A=[a10a], then A^(n)=[a^(n)a^(n-1)0a^(n)] for every positive integer n .

A=[{:(a,b),(0,1):}],ane1 then prove that A^(n)=[{:(a^(n),(b(a^(n)-1))/(a-1)),(0," "1):}], n inN .

If A={:[(1,1,1),(0,1,1),(0,0,1)] , Prove by mathematical induction that, A^(n)={:[(1,n,(n(n+1))/2),(0,1,n),(0,0,1)] for every positive integer n.