It is dependent on the theme you are using. On many themes, all the post metadata is controlled in one place in the CSS, so if you hide one, you can hide all (date, categories, author, date, “make a comment link,” and in some themes you even lose the post title.
IF the theme you are using has the author and date controlled separately, it would require that you have experience editing CSS, and the paid CSS upgrade.
Please don’t purchase the upgrade if you do not have at least a general understanding of CSS and are sure that it can be done with your theme. There is a “preview” function in the CSS edit page where you can try changes.