counting - Count Column Elements in a Matrix

Let a square matrix be:

mat={{1,2,3},{4,5,6},{0,0,0}};

Get a total for each column:

In: Total[mat]

Out: {5,7,9}

I would like to obtain the number of non-zero elements of each column (and the result to be in the form {a,b,c}).

Thanks

Answer

I think the simplest version is:

Total @ Unitize @ mat

{2, 2, 2}