row major and column major major confusion

Capturing for posterity:

TL;DR: C is row major, XMMATRIX* is row major, HLSL is column major. 

A comment here explains rationale:

https://www.gamedev.net/forums/topic/649263-matrix-multiplication-order/

And you can tell HLSL to flip to row major.

Buffers

 read this: http://www.joshbarczak.com/blog/?p=1260