Inverse matrix in a relation

1. Nov 5, 2006

Hi .
I have this question( discrete math) :
How can the matrix for R-1 , the inverse of the relation R, be found from the matrix representing R, when R is a relation a finite set A.

How can I do this problem?

2. Nov 6, 2006

HallsofIvy

Staff Emeritus
When in doubt, try a simple example. Suppose A= {1, 2, 3} and R is defined as {(1, 1), (1, 3), (2, 3)} (I just made that up pretty much at random. Remember that a "relation on A" is just a collection of pairs of members of A.) Now, the "matrix representing R" is the matrix having 1 in the "a row, b column" when (a,b) is in R, 0 otherwise. here, labeling the rows and columns 1, 2, 3 in that order, the matrix is
$$\left(\begin{array}{ccc}1 & 0 & 1\\0 & 0 &1 \\0 & 0 & 0\end{array}\right)$$.

What is the relation R-1? What matrix represents it? How are the two matrices related?

3. Nov 6, 2006