There was a problem to make a shadow and reflection of the object on invisible plane using Mental Ray's Matte/Shadow/Reflection material. After browsing and reading stuff I've found a good Jeff Patton's idea for Maya which I adopted for 3DS Max.
So, as usual use a plane with Matte/Shadow/Reflection material. To make it invisible use Environment background Switcher map on it's Camera Mapped background slot and on Environment slot of a scene, for example I had an HDRI map and gray background. Gray background is generated with Composite map, though the colour of the back can be set to any colour, read on to know why.
Do not forget to enable Process background and environment map in Exposure Control to avoid black plane (due to difference in exposure control).
If you render yur scene now, you get this. You see opaque plane with white (maximum opacity) alpha.
So to get rid of this, and to get rid of plane's own unneeded alpha channel you have to pass manually generated empty alpha into the Composite map (along with any colour).
Voilà, you got it, the only thing you miss is the main map's colour, but now with proper background alpha channel you can make it any colour you want.