Thus, the matrix (w.r.t. any basis) of an invertible linear application is a square matrix. Denote by A the
matrix of
w.r.t. some bases of U and V; the matrix of
is A^{-1}.
How to compute A^{-1}?
The sequence of elementary operations which transforms the matrix A into the
matrix I transforms also the matrix I into the matrix A^{-1}.