If `A=diag [a,b,c]` then show that `A^n=diag[a^n,b^n,c^n]` for all `n in N.`

If A = diag [{:(a,b,c):}] , then show that A^(n)="diag"[{:(a^(n),b^(n),c^(n)):}],AAn in N .

If A=diag(abc), show that A^(n)=diag(a^(n)b^(n)c^(n)) for all positive integer n .

If A=diag(abc), show that A^(n)=diag(a^(n)b^(n)c^(n)) for all positive integer n.

If A=d i ag\ (a\ \ b\ \ c) , show that A^n=d i ag\ (a^n\ \ b^n\ \ c^n) for all positive integer n .

If a,b,c,d are in G.P. prove that (a^n+b^n),(b^n+c^n),(c^n+d^n) are in G.P.

If a ,b ,c,d are in G.P. prove that (a^n+b^n),(b^n+c^n),(c^n+d^n) are in G.P.

If a ,b ,c,d are in G.P. prove that (a^n+b^n),(b^n+c^n),(c^n+d^n) are in G.P.

If a ,b ,c,d are in G.P. prove that (a^n+b^n),(b^n+c^n),(c^n+d^n) are in G.P.

If B, C are a rowed squre matrices and if A=B+C, BC= CB, C^2=0, then show that A^(n-)=B^n(B+(n+1)C)AA^nin N.

If a,b,c,d are distinct positive then a^n/b^ngtc^n/d^n for all epsilon N if a,b,c,d are in (A) A.P. (B) G.P. (C) H.P. (D) none of these