The matrix feature today has an IR pass that can toggle between row major and column major.
This flag is exposed in opt and somlir-opt and opt can both be used to invoke -matrix-default-layout=column-major or -matrix-default-layout=row-major.
What we need is the clang driver to add -mllvm -matrix-default-layout=*-major so the existing matrix pass will shift its major order.
This needs to be a cc1 flag. It will also block us from starting #166410.