Only easting-northing (or longitude-latitude) ordered coordinate reference systems are supported in ArcGIS software so far. There are enhancement requests to support other variations. You can emulate the system by defining it, but making the scale factor equal to negative 1.0 rather than positive 1.0.
(I thought it was also a right-handed system, at least how I was taught in a Physics class to figure it out. It's westing-southing, so "point your open hand in the first axis direction, bend your fingers towards the 2nd axis, and an out-thrust thumb will point in the 3rd axis direction")
