On the set of mappings of the given set, we define the product of mappings.
If A is associative algebra, then we consider the set of matrices, whose
elements are linear mappings of algebra A. In algebra of matrices of linear
mappings we define the operation of product. The operation is based on the
product of mappings.

If the matrix a of linear mappings has an inverse matrix, then the
quasideterminant of the matrix a and the inverse matrix are matrices of linear
mappings. In the paper, I consider conditions when a matrix of linear mappings
has inverse matrix, as well methods of solving a system of linear equations in
an associative algebra.