Dimension Reduction reduces row or column in Random projection

I know the concept of random projection where the original matrix M x N is multiplied with the random matrix N X K [where K is smaller than N] so we get reduced matrix M X K. In many articles, they mentioned that Dimension reduction is always reducing the columns. Can we apply random projection for rows?

PS: I know that if we take the transpose of matrix rows becomes columns and we do the same operation. but my question is whether the dimension reduction by random projection is column oriented only?