The aim of this paper is to study some aspects of matrix theory through Pasting and Reversing.We start giving a summary of previous results concerning to Pasting and Reversing over vectors and matrices, after we rewrite such properties of Pasting and Reversing in matrix theory using linear mappings to finish with new properties and new sets in matrix theory involving Pasting and Reversing.In particular we introduce new linear mappings: Palindromicing and Antipalindromicing mappings, which allow us to obtain palindromic and antipalindromic vectors and matrices.