From what I've seen looking around, it appears that:
Given a relation matrix, I can find its *transitive closure* by multiplying it by itself multiple times until the multiplication ceases to change the matrix.
For example: Given the relation matrix A, calculate $A^n$ until $A^n = A^{n-1}$ and the final non-changing $A^n$ is the transitive closure of A.
Is that all correct?