Journal of Formalized Mathematics
Volume 4, 1992
University of Bialystok
Copyright (c) 1992 Association of Mizar Users

## Transpose Matrices and Groups of Permutations

Katarzyna Jankowska
Warsaw University, Bialystok

### Summary.

Some facts concerning matrices with dimension $2\times 2$ are shown. Upper and lower triangular matrices, and operation of deleting rows and columns in a matrix are introduced. Besides, we deal with sets of permutations and the fact that all permutations of finite set constitute a finite group is proved. Some proofs are based on [11] and [14].

#### MML Identifier: MATRIX_2

The terminology and notation used in this paper have been introduced in the following articles [15] [8] [20] [21] [5] [7] [6] [2] [18] [19] [4] [17] [13] [3] [1] [12] [10] [16] [9]

#### Contents (PDF format)

1. Some examples of matrices
2. Deleting of rows and columns in a matrix
3. Sets of permutations
4. Group of permutations

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