"To study the matter" means to carefully examine or investigate a particular topic or issue in order to gain knowledge and understanding about it. Full definition
I am not a scholar by any means so I will quote someone who has studied this matter far more than I have. (religion.blogs.cnn.com)
Computer simulations offer the possibility to study matter with microscopic detail and predict properties solely based on an accurate description of molecular interactions. (molssi.org)
I know there has to be a story behind this, but I have not studied the matter. (davidmarkbrownwrites.com)