Let A,B belong to Mn and AB=BA. Let p(•) be any polynomial, say of degree m. Show that p(A)p(B) = p(B)p(A).

The only thing that I have in my notes states that

pA(t)=(t-http://www.physlink.com/Images/symbols/lambda.gif1)(t-http://www.physlink.com/Images/symbols/lambda.gif2)...(t-http://www.physlink.com/Images/symbols/lambda.gifn).

I have no idea even how to begin this. Any help would be great. Thanks!