#### Name

Khlon Ivan Dmitrievich

#### Scholastic degree

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#### Academic rank

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#### Honorary rank

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#### Organization, job position

Kuban State Agrarian University

#### Web site url

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## Articles count: 1

The inverse matrix for the square matrix A of order n
with coefficients of some field exists, as it is known
then and only then, when its determinant is not equal to
zero. If the matrix A has a certain type (certain
structure), then an inverse matrix A-1 should not have
exactly the same structure. Therefore, it is interesting
to describe such square matrices A, which have an
inverse matrix A-1, having the same structure as the
matrix A, under certain conditions. For example, a
subdiagonal matrix with nonzero elements on the main
diagonal has an inverse matrix over a field of
characteristic zero, having also the form of subdiagonal
matrix. Similarly, an inverse matrix towards
symmetrical or skew-symmetric matrix is also
symmetric or skew-symmetric accordingly. Also, the
matrix inverse to non-degenerate (nonsingular)
circulant will be a circulant itself, and finally, the
matrix inverse to nonsingular quasdiagonal matrix D
will be quasdiagonal itself, and will have the same
partitioned structure as D. Thus, there is a problem of
determining these types of nonsingular matrices that
have an inverse matrix of the same type as a given
matrix. In line with this problem in the present study it
is determined such type of matrices for which an
inverse matrix has the same type, at that the conditions
are identified in explicit form, ensuring the
nonsingularity of the matrix. The matrices of three
orders are shown in detail. These results allow
determining the characteristics of fields over which
there are inverse matrices of the considered types