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The General operation of Matrices is an original study introduced by the author in the mathematical domain. The basic idea of the General operation of Matrices is similar to the traditional operation of matrices, but moreover the General operation of Matrices is more general and contains many forms and ways of multiplying, adding, subtracting and dividing many matrices. The main goal of introducing the General operation of Matrices is to facilitate the writing of many complicated equations in simple matrices. In this paper a brief study is introduced with the definition of the General operation of Matrices and simple applications are developed in order to give idea about the importance of this new concept of operation between Matrices. Many studies will follow this one in order to find more applications in mathematics and all scientific domains.