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This paper discussed the matrix of elementary transformation in the higher elementary algebra linear algebra and number theory in wide use. Matrix is the main basis for the elementary transformation in the transformation of the matrix before and after to maintain the same rank, including the Matrix will transform the primary and elementary transformation shown in elementary transformation. Here mainly to elementary transformation as an example. First, the matrix of elementary transformation in the use of advanced algebra in a very wide and easy to use. Can be used to inverse matrix, and Vector Group's nothing to do great group that Vector Group equivalent, of linear equations, and the judgement of the matrix equation Vector Group's linear, and so on. Secondly, linear algebra, can create a polynomial coefficient and multiple lines between the matrix-style counterparts, so as to transform line for the primary use of the domain P polynomial the greatest common factor. In addition, elementary number theory, the matrix also can be used for elementary transformation to bring more than once and the division of congruence, and promotion to general-in addition to polynomial. Finally the elementary transformation in the block matrix in the promotion, and an example.