  The matrices and their sub-blocks are introduced into the study of
determining various extensions in the sense of Dung's theory of argumentation
frameworks. It is showed that each argumentation framework has its matrix
representations, and the core semantics defined by Dung can be characterized by
specific sub-blocks of the matrix. Furthermore, the elementary permutations of
a matrix are employed by which an efficient matrix approach for finding out all
extensions under a given semantics is obtained. Different from several
established approaches, such as the graph labelling algorithm, Constraint
Satisfaction Problem algorithm, the matrix approach not only put the mathematic
idea into the investigation for finding out various extensions, but also
completely achieve the goal to compute all the extensions needed.
