  A new matrix operation based on inserting columns and rows, similarly to the
mediant operation between fractions, gives rise to the Farey determinants
matrix or, equivalently, the matrix of the numerators of the differences of
Farey fractions. This matrix allows to visualize established properties and
theorems of Farey fractions allowing for more intuitive demonstrations and
easier understanding. Furthermore it is shown how some Farey determinants
matrices contain other lower order Farey determinants matrices as block
matrices around the main diagonal.
