After we have introduced the concepts of a matrix, matrix equality, and the basic types of matrices, in this chapter we introduce basic operations with matrices. Four basic binary operations are defined in the set of real numbers: addition, subtraction, multiplication, and division. Therefore, we want to introduce their equivalents to the set of matrices, with similar properties as the corresponding binary operations in the set of real numbers. Thus, we introduce the operations of addition, subtraction, multiplication by a scalar, scalar product, and matrix multiplication in the set of matrices. Instead of the operation of division, we introduce the concepts of inverse and multiplication with inverse.