The computation of the diagonal of the inverse of a matrix appears also in graph theory, machine learning, electronic structure calculations, and portfolio analysis, and various methods are proposed in the literature for this task [4, 21].

The trace of the inverse of a matrix is required in several applications arising from the fields of statistics, fractals, lattice quantum chromodynamics, crystals, network analysis, and graph theory [7, 8, 14].

Secondary school teachers may use this activity to consolidate their students' learning of certain concepts of matrices such as the algorithm for matrix multiplication and the concept of the multiplicative inverse of a matrix.

For instance, teachers can teach students to make use of the functions such as MMULT, MDETER and MINVERSE in Microsoft Excel to perform matrix multiplication, as well as to find the determinant and inverse of a matrix.

The case q = -1, which leads to estimates of the trace of the inverse of a matrix, was studied in [4]; on this problem, see [10].

This idea was introduced in [3] for estimating the norm of the error in the solution of a system of linear algebraic equations, and it was used in [4] for estimating the trace of the inverse of a matrix.

1](z) given in [4], which leads to the estimate of the trace of the inverse of a matrix.

which leads to the two-term estimate given in [4] for the trace of the inverse of a matrix.

4, the structure of the inverse of a matrix F is given by the transitive closure of the directed graph of the transposed matrix [F.

4 that the directed graph of the inverse of a matrix is the transitive closure of the directed graph corresponding to the matrix.