If we define MATTER as the thing that gives concreteness and shape to the 3-D world, creating a substrate layer and IDEA as the notion that is pure information that does not depend on its substrate, similar to what hardware and software are for computing:
a) The root of all cannot be simple matter. Matter does not account for inner/psychic phenomena and experience/consciousness, the quality of the world.
b) The root of all cannot be simply an idea. An idea cannot be a substratum itself; how can an idea be processed, exist on its own, without matter or substance?
The definition of the two terms is begging the question directly, but it seems true that in case we experience or define the world in this dualistic sense of matter/idea, body/mind, hardware/software, which most of us do, then we are on the right path to create contradictions.
The most certain conclusion leveraging our current knowledge is that the root of existence is a PARADOX relative to our current understanding and reasoning. We can never reach it with classical logic, Aristotelian syllogisms, current mathematics etc.
Philosophical, theological and logical inquiries point to similar antinomies. Infinite regress, acausal cause, first unmoved mover, the thing that cannot be comprehended.