How does the distinctness of values in a matrix A affect its determinant?

[mathbug]

Homework Statement

Let a1, a2, ..., an live in R. Prove that the equation

det [ A ] = 0

where A:
1 x x^2 ... x^n
1 a1 a1^2 ... a1^n
1 a2 a2^2 ... a2^n
. . . . .
. . . . .
. . . . .
1 an an^2 ... an^n

has exactly n solutions if and only if the a1, ..., an are distinct; i.e. ai=/=aj for all i=/=j

Homework Equations

None

The Attempt at a Solution

Well, my problem is that I don't even know where to really start. So my attempts at a solution don't exactly make much sense. I was just playing around hoping I would come up with something, which I didn't

 

[ystael]

What property of a matrix $$A$$ ensures that its determinant is zero (or, inversely, not zero)? How does this property connect to the relationships between the rows (or columns) of $$A$$?