Bordered matrices and some their applications

In this paper bordered matrices and some their applications are presented. In particular we give information how can be found matrix F = AB-1C without calculation the inverse of matrix B (when B = I this way we obtain Cauchy's product of matrices A and C). We present how to find generalized inverse of the Moore'a-Penrose'a type too and finally calculate value of determinant of given matrix A of order nxn.(original abstract)