Why is one eigenvalue of this matrix necessarily zero?

Question

I have a 400x4096 matrix M. If I do M^TM, I get a 4096x4096 matrix. If I find the eigenvalues of this matrix, there are 399 non-zero eigenvalues. Even if I change the values in the original matrices, I find that there are always 399 non-zero eigenvalues.

What I Want To Know:

1) I assume that the 399 comes from the 400 in the original matrix, and that two of the rows are not linearly independent, so we get 400 eigenvalues, of which one is zero. Is this the case?

2) If so, why are two of the rows linearly dependent? ie. why do we get 399 instead of 400?