Is the original tile the sort of figure 8 made of 2 triangles? If that's a single object, then Inkscape can show you the center of rotation. Select with Selection tool
, then just click on it for a 2nd time. You'll notice that the arrows change from scaling to rotation arrows. And also a plus sign appears where the rotation center is.
If those are 2 separate triangles, you can still find the rotation center by selecting both of them. Then again, click a 2nd time.
If it's a group, the group acts just like a single object.
Or are you asking how to find the rotation center of the single unit, while it's in the array? That would depend on what kind of objects they are. Are they in a group? Are they still individual objects?