vandermonde matrix question

Let T: P_n(F)->F^(n+1) be the linear transformation defined
by T(f)=(f(c_o), f(c_1), ... , f(c_n)), where
c_o, c_1, ..., c_n are distinct scalars in the infinite
field F. Let B be the standard ordered basis for P_n(F)
and y be the standard ordered basis for F^(n+1).

1) How can I show that M=[T]y,B has the form:
[1 c_o (c_o)^2 ... (c_o)^n
1 c_1 (c_1)^2 ... (c_1)^n
.
.
.
1 c_n (c_n)^2 ... (c_n)^n]


2) How can I use the fact that I know that T is an
isomorphism to prove that det(M)=/0? (doesn't equal 0)

3) How can I show that det(M)= [product] ((c_j)-(c_i))?

Thanks!
.