[R] degree of freedom of interaction effect

[genomenet at gmail.com]

Hi There,

Suppose two factors, A and B.
A has n levels, B has m levels.

Why the degree of freedom of interaction effect of A and B ( here I
mean A:B not A*B) is (n-1)*(m-1) not n*m-1?

I know this is a basic statistical question. Please recommend some
good websites or books.

Thank you very much.

Fan