Hypergraph matching

In computational complexity theory, 3-Dimensional Matching is one of the famous Karp's 21 NP-complete problems. The problem can be formalized as:

Given $T\subseteq X\times Y\times Z$, and $X,Y,Z$ are disjoint. Does there exist a mathcing $M\subseteq T$ such that each element of $X,Y,Z$ exists in exactly one set of $M$?

Note that two-dimensional matching, known as bipartite matching, is solvable in polynomial time. But any dimension higher than 3, is in NP.