  For a two-parameter family of lower triangular matrices with entries
involving Jacobi polynomials an explicit inverse is given, with entries
involving a sum of two Jacobi polynomials. The formula simplifies in the
Gegenbauer case and then one choice of the parameter solves an open problem in
a recent paper by Koelink, van Pruijssen & Roman. The two-parameter family is
closely related to two two-parameter groups of lower triangular matrices, of
which we also give the explicit generators. Another family of pairs of mutually
inverse lower triangular matrices with entries involving Jacobi polynomials,
unrelated to the family just mentioned, was given by J. Koekoek & R. Koekoek
(1999). We show that this last family is a limit case of a pair of connection
relations between Askey-Wilson polynomials having one of their four parameter
in common.
