How to use the prod function on non-zero elements?

I have a matrix with zeros in its main diagonal. I would like to take the product of the elements in each row (excluding the 0) so as to get a column vector. How can I make it using a vectorized code? E.g.

A = [0 1 2; 2 0 4; 7 8 0];

I want to get:

[1*2; 2*4; 7*8]

Thank you.

Answer 1

[Azzi Abdelmalek]

A = [0 1 2; 2 0 4; 7 8 0];
B=A
B(~A)=1  % replace 0 elements by 1 
out=prod(B,2)

[Zoltán Csáti]

How stupid I am! I should have thought of it. Thank you very much.