  In this paper, we present a novel method to compute an explicit formula for
the inverse of the confluent Vandermonde matrices. Our proposed results may
have many interesting perspectives in diverse areas of mathematics and natural
sciences, notably on the situations where the Vandermonde matrices have
acquired much usefulness. The method presented here is direct and
straightforward, it gives explicit and compact formulas not exist in the large
literature on this essential topic. Several examples are presented to highlight
the results. Our main tools are some elementary basic linear algebra.
